Empirical study on the factors that induce jumps in interest rates in the euro area is still missing. In this paper, maximum likelihood estimates of I-distribution parameters are extracted using as a first step, an or...Empirical study on the factors that induce jumps in interest rates in the euro area is still missing. In this paper, maximum likelihood estimates of I-distribution parameters are extracted using as a first step, an original linear model. According to the contribution of ([1] [2]) in the case of developing a class of Poisson-Gaussian model, we try to enhance the predictive power of this model by distinguishing between a pure Gaussian and Poisson-Gaussian distributions. Such an empirical tool permits to optimizing results through a comparative analysis dealing with the fluctuation of the Euro-interbank offered rate and its statistical descriptive behaviour. The analytical and empirical methods try to evaluate the behavioural success of the ECB intervention in setting interest rates for different maturities. Jumps in euribor interest rate can mainly be linked to surprise decisions of the European Central Bank, and the too frequent meetings of the ECB before November 2001. Despite this special event that leads to a certain lack of predictability, other few day-of-week effects are modelled to prove eventual evidence of bond market overreaction. Empirical results prove that Mondays and Wednesdays are the preponderant days. Regarding monetary policy, negative surprises induce larger jumps than positive ones.展开更多
Fractional calculus and fractional-order modeling provide effective tools for modeling and simulation of anomalous diffusion with power-law scalings.In complex multi-fractal anomalous transport phenomena,distributed-o...Fractional calculus and fractional-order modeling provide effective tools for modeling and simulation of anomalous diffusion with power-law scalings.In complex multi-fractal anomalous transport phenomena,distributed-order partial differential equations appear as tractable mathematical models,where the underlying derivative orders are distributed over a range of values,hence taking into account a wide range of multi-physics from ultraslow-to-standard-to-superdiffusion/wave dynamics.We develop a unified,fast,and stable Petrov–Galerkin spectral method for such models by employing Jacobi poly-fractonomials and Legendre polynomials as temporal and spatial basis/test functions,respectively.By defining the proper underlying distributed Sobolev spaces and their equivalent norms,we rigorously prove the well-posedness of the weak formulation,and thereby,we carry out the corresponding stability and error analysis.We finally provide several numerical simulations to study the performance and convergence of proposed scheme.展开更多
The authors consider the problem of reaching consensus over a communication network via asynchronous interaction between pairs of agents.A well-known method is the linear gossip algorithm due to Tsitsiklis(1984).Exten...The authors consider the problem of reaching consensus over a communication network via asynchronous interaction between pairs of agents.A well-known method is the linear gossip algorithm due to Tsitsiklis(1984).Extension of this,allowing the selection of a strictly stationary sequence of communicating pairs,was given in Picci and Taylor(2013).Extension of the linear gossip algorithm to directed communication networks,retaining the linear dynamics,was proposed by Cai and Ishii(2012),later extended by Silvestre,et al.(2018).A definite novelty of these algorithms is that L2-convergence with exponential rate can be established.The authors attend the above issues,extending the result of Picci and Taylor(2013)motivated by features of algorithms for directed networks.The authors present and discuss the algorithm of Silvestre,et al.(2018),together with systematic simulation results based on 5M randomly chosen parameter settings.The core of the proposed mathematical technology is a set of simple observations,presented with a tutorial aspect,by which the authors can conveniently establish various results on the almost sure convergence of products of strictly stationary sequences of matrices to a rank-1 matrix.展开更多
After one year＇s delay due to the big earthquake in 2011, the Second Institute of Mathematical Statistics Asia Pacific Rim Meeting （IMS-APRM） was held in Tsukuba, Japan, in July of 2012. As a member of the Scientif...After one year＇s delay due to the big earthquake in 2011, the Second Institute of Mathematical Statistics Asia Pacific Rim Meeting （IMS-APRM） was held in Tsukuba, Japan, in July of 2012. As a member of the Scientific Committee of the meeting, I was responsible to mobilize participants from China and to recommend invited speakers. My inexperience in fulfilling the task was easily compensated by the enthusiasm of my colleagues. More than 10 statisticians and probabilists from the mainland of China gave invited talks. In particular, Professor Zhi Geng of Peking University delivered a Distinguished Lecture. Recent progress in probability and statistics in China was well presented. When I was asked by the Editor in Chief, Professor K. -C. Chang, to compile a special issue for Frontiers of Mathematics in China, I once again turned to the speakers for help.展开更多
In many lifetime studies, some of the subjects under study are censored on the righ bya prior censoring time. We observe only the censored data. It is important to estimatethe life characteristics of the subjects. Let...In many lifetime studies, some of the subjects under study are censored on the righ bya prior censoring time. We observe only the censored data. It is important to estimatethe life characteristics of the subjects. Let T<sub>1</sub>, T<sub>2</sub>,…, T<sub>n</sub> be independent and identically dis-tributed nonnegative random variables with common continuous distribution funtion F展开更多
Here we study the problems of local asymptotic normality of the parametric family of distri-butions and asymptotic minimax efficient estimators when the observations are subject to right censor-ing. Local asymptotic n...Here we study the problems of local asymptotic normality of the parametric family of distri-butions and asymptotic minimax efficient estimators when the observations are subject to right censor-ing. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and fur-thermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.展开更多
A number of researching works have shed light on the field of complex networks recently. We investigate a wide range of real-world networks and find several interesting phenomena. Firstly, almost all of these networks...A number of researching works have shed light on the field of complex networks recently. We investigate a wide range of real-world networks and find several interesting phenomena. Firstly, almost all of these networks evolve by overlapping new small graphs on former networks. Secondly, not only the degree sequence of the mature network follows a power-law distribution, but also the distribution of the cumulative occurrence times during the growing process are revealed to have a heavy tail. Existing network evolving models do not provide interpretation to these phenomena. We suggest a model based on the team assembling mechanism, which is extracted from the growing processes of real-world networks and requires simple parameters, and produces networks exhibiting these properties observed in the present study and in previous works.展开更多
We give a new way to price American options by using Samuelson’s formula. We first obtain the option price corresponding to a European option at time t, weighing it by the probability that the underlying asset takes ...We give a new way to price American options by using Samuelson’s formula. We first obtain the option price corresponding to a European option at time t, weighing it by the probability that the underlying asset takes the value S at time t. We then use Samuelson’s formula with this factor which is given by the solution of the Fokker-Planck (Kolmogorov) equation for the transition probability density. The main advantage of this approach is that we can systematically introduce the effect of macroeconomic factors. If a macroeconomic framework is given by a dynamical system in the form of a set of ordinary differential equations we only have to solve a partial differential equation for the transition probability density. In this context, we verify, for the sake of consistency, that this formula coincides with the Black-Scholes model and compare several numerical implementations.展开更多
Let B be a separable real Banach space and m be a positive measure on B. In this paper, we will establish the Beurling-Deny formulae of the Dirichlet forms on L~2(B, dm).
Background It is well recognized that meteorological factors have important influences on the onset and development of many kinds of diseases. The present study was undertaken to investigate the effects of the meteoro...Background It is well recognized that meteorological factors have important influences on the onset and development of many kinds of diseases. The present study was undertaken to investigate the effects of the meteorological elements on admission rates of cerebral infarction patients with hypertensive nephropathy at Changchun city, Jilin Province, northeast China. Methods A total of 763 medical records of inpatients from nine hospitals at Changchun city, during a period from April 6 to April 17 in 2010, were reviewed. These patients were admitted to hospitals due to the occurrence of cerebral infarction. The hypertensive nephropathy was evidenced with certain diagnosis of essential hypertension and hypertension-related kidney injuries. The cerebral infarction was diagnosed according to the World Health Organization （Stroke） standard. All the meteorological data were from practical monitoring records in Jilin Province Meteorological Observatory. The relationships between the epidemiological prevalence of cerebral infarction and meteorological variables were analyzed using the time series models of statistics. Results Compared with admission rates before the violent change in meteorological status （April 6 to April 17, 2010）, the number of admission patients suffering from cerebral infarction remarkably peaked on April 12. Such an increase was highly correlated with heavy precipitation, elevation of daily average relative humidity, and reduction of average daily air temperature. With the betterment of the meteorological conditions on April 17, the admission rates of cerebral infarction patients dropped to the same level as the dates before snowing （April 6 to April 11）. Conclusions The meteorological changes are highly associated with the occurrence of cerebral infarction in patients with hypertensive renal injury in northeast China. This study also suggested that an intensive medical interference for those patients with hypertension-induced organ injuries is very necessary in preventing the occurrence of cerebral infarction with hypertensive nephropathy when there is a violent change in meteorological condition展开更多
For the fixed design regression modelwhen Y, are randomly censored on the right, the estimators of unknown parameter and regression function g from censored observations are defined in the two cases .where the censore...For the fixed design regression modelwhen Y, are randomly censored on the right, the estimators of unknown parameter and regression function g from censored observations are defined in the two cases .where the censored distribution is known and unknown, respectively. Moreover, the sufficient conditions under which these estimators are strongly consistent and pth (p>2) mean consistent are also established.展开更多
A family of irreducible Markov chains on a finite state space is considered as an exponential perturbation of a reducible Markov chain. This is a generalization of the Freidlin-Wentzell theory, motivated by studies of...A family of irreducible Markov chains on a finite state space is considered as an exponential perturbation of a reducible Markov chain. This is a generalization of the Freidlin-Wentzell theory, motivated by studies of stochastic Ising models, neural network and simulated annealing. It is shown that the metastability is a universal feature for this wide class of Markov chains. The metastable states are simply those recurrent states of the reducible Markov chain. Higher level attractors, related attractive basins and their pyramidal structure are analysed. The logarithmic asymptotics of the hitting time of various sets are estimated. The hitting time over its mean converges in law to the unit exponential distribution.展开更多
Suppose that the patients’ survival times,Y,are random variables following the semiparametric regression model Y=Xβ+g(T)+ε,where (X,T) is a radom vector taking values in R×[0,1],β is an unknown parameter,g(&#...Suppose that the patients’ survival times,Y,are random variables following the semiparametric regression model Y=Xβ+g(T)+ε,where (X,T) is a radom vector taking values in R×[0,1],β is an unknown parameter,g(·) is an unknown smooth regression function and εis the random error with zero mean and variance σ2.It is assumed that (X,T) is independent of ε.The estimators βn and gm(·) ofβ and g(·) are defined,respectively,when the observations are randomly censored on the right and the censoring distribution is unknown.Moreover,it isshown that βm is asymptotically normal and gm(·) is weak consistence with rate Op(n-1/3).展开更多
For regression analysis, some useful information may have been lost when the responses are right censored. To estimate nonparametric functions, several estimates based on censored data have been proposed and their con...For regression analysis, some useful information may have been lost when the responses are right censored. To estimate nonparametric functions, several estimates based on censored data have been proposed and their consistency and convergence rates have been studied in literature, but the optimal rates of global convergence have not been obtained yet. Because of the possible information loss, one may think that it is impossible for an estimate based on censored data to achieve the optimal rates of global convergence for nonparametric regression, which were established by Stone based on complete data. This paper constructs a regression spline estimate of a general nonparametric regression function based on right-censored response data, and proves, under some regularity conditions, that this estimate achieves the optimal rates of global convergence for nonparametric regression. Since the parameters for the nonparametric regression estimate have to be chosen based on a data driven criterion, we also obtain the asymptotic optimality of AIC, AICC, GCV, CP, and FPE criteria in the process of selecting the parameters.展开更多
The closed form of the entropy production of stationary diffusion processes with bounded Nelson’s current velocity is given.The limit of the entropy productions of a sequence of reflecting diffusions is also discussed.
Consider the partially linear modelY<sub>i</sub>=X<sub>i</sub><sup>τ</sup>β<sub>0</sub>+ g<sub>0</sub>（T<sub>i</sub>）+e<sub>i</sub&g...Consider the partially linear modelY<sub>i</sub>=X<sub>i</sub><sup>τ</sup>β<sub>0</sub>+ g<sub>0</sub>（T<sub>i</sub>）+e<sub>i</sub>,where （T<sub>1</sub>, X<sub>1</sub><sup>τ</sup>, Y<sub>1</sub>）,…,（T<sub>n</sub>,X<sub>n</sub><sup>τ</sup>, Y<sub>n</sub>） are i. i. d. observations of a random （d+2）-vector （T,X<sup>τ</sup>, Y）, X=（x<sub>1</sub>,…,x<sub>d</sub>）<sup>τ</sup> is a d-vector of explanatory variables, β<sub>0</sub> is a vector of unknownparameters, T is another explanatory variable ranging over a nondegenerate compactinterval, say [0, 1],g<sub>0</sub>（·）is an unknown smooth function, and e<sub>i</sub>’s are random errors.展开更多
Consider a stable AR model of two parameter spatial series {X<sub>t</sub>, t∈N<sup>2</sup>}, i. e. {X<sub>t</sub>t∈N<sup>2</sup>} is homogeneous and satisfies the foll...Consider a stable AR model of two parameter spatial series {X<sub>t</sub>, t∈N<sup>2</sup>}, i. e. {X<sub>t</sub>t∈N<sup>2</sup>} is homogeneous and satisfies the following difference equationX<sub>t</sub>-sum from n=s∈【v,p] to a<sub>s</sub>X<sub>t-s</sub>=W<sub>t</sub> （t∈N<sup>2</sup>）where {W<sub>t</sub>, t∈N<sup>2</sup>} is a two parameter white noise and the notation【3, p] expresses the set of two dimentional lattice points {（k<sub>1</sub>, k<sub>2</sub>）: 0≤k<sub>1</sub>≤p<sub>1</sub>, 0≤k<sub>2</sub>≤p<sub>2</sub> but （k<sub>1</sub>, k<sub>2</sub>）≠（0, 0）}, and furthermore the two-variable polynomial1-sum from n=（s<sub>1</sub>,s<sub>2</sub>）∈【0,p] a（s<sub>1</sub>,s<sub>2</sub>） Z<sub>1</sub><sup>k</sup><sub>1</sub>Z<sub>2</sub><sup>s</sup><sub>2</sub>≠0（|Z<sub>1</sub>|≤1,|Z<sub>2</sub>|≤1）.In this paper, under frirly general conditions （it is required that {W<sub>t</sub>} Satisfies the conditions of two-parameter martingale difference, which is much weaker than supposing {W<sub>t</sub>} to be i. i. d.）, the author obtains strong consistency and asymptotic normality of the Y-W （LS） estimate of the AR parameters {a<sub>s</sub>} whenever n<sub>1</sub>n<sub>2</sub>→∞, where n<sub>1</sub> and denote the horizontal and vertical sampling width respectively.展开更多
Suppose that (x_t,t≥0) is a stochastic process of the exponential type with P_θ(x_t∈B) =∫_B exp{θ_x - tψ(θ)}γ(t,x)V_t(dx),where θ∈Θ? (-∞,∞) and V_t is a measure. For testing the hypothesis θ≤θ_0 agains...Suppose that (x_t,t≥0) is a stochastic process of the exponential type with P_θ(x_t∈B) =∫_B exp{θ_x - tψ(θ)}γ(t,x)V_t(dx),where θ∈Θ? (-∞,∞) and V_t is a measure. For testing the hypothesis θ≤θ_0 againstθ>θ_0, we have found a class of truncated sequential tests with probability of the first kindof error not exceeding α, the expected observation time of tests being asymptoticallyminimal as α ↓0.展开更多
The conventional method for testing hypotheses is to find an exact or asymptotic distributionof a test statistic. But when the model is complex and the sample size is small, difficulty often arises. Thispaper aims to ...The conventional method for testing hypotheses is to find an exact or asymptotic distributionof a test statistic. But when the model is complex and the sample size is small, difficulty often arises. Thispaper aims to present a method for finding maximum probability with the help of EM algorithm. For any fixedsample size, this method can be used not only to obtain an accurate test but also to check the real level ofa test which is build by large sample theory. Especially, while doing this, one needs neither the accurate norasymptotic distribution of the test statistic. So the method is easily performed and is especially useful for small samples.展开更多
文摘Empirical study on the factors that induce jumps in interest rates in the euro area is still missing. In this paper, maximum likelihood estimates of I-distribution parameters are extracted using as a first step, an original linear model. According to the contribution of ([1] [2]) in the case of developing a class of Poisson-Gaussian model, we try to enhance the predictive power of this model by distinguishing between a pure Gaussian and Poisson-Gaussian distributions. Such an empirical tool permits to optimizing results through a comparative analysis dealing with the fluctuation of the Euro-interbank offered rate and its statistical descriptive behaviour. The analytical and empirical methods try to evaluate the behavioural success of the ECB intervention in setting interest rates for different maturities. Jumps in euribor interest rate can mainly be linked to surprise decisions of the European Central Bank, and the too frequent meetings of the ECB before November 2001. Despite this special event that leads to a certain lack of predictability, other few day-of-week effects are modelled to prove eventual evidence of bond market overreaction. Empirical results prove that Mondays and Wednesdays are the preponderant days. Regarding monetary policy, negative surprises induce larger jumps than positive ones.
基金This work was supported by the AFOSR Young Investigator Program(YIP)award(FA9550-17-1-0150),the MURI/ARO(W911NF-15-1-0562)tthe National Science Foundation Award(DMS-1923201)the ARO Young Investigator Program Award(W911NF-19-1-0444)。
文摘Fractional calculus and fractional-order modeling provide effective tools for modeling and simulation of anomalous diffusion with power-law scalings.In complex multi-fractal anomalous transport phenomena,distributed-order partial differential equations appear as tractable mathematical models,where the underlying derivative orders are distributed over a range of values,hence taking into account a wide range of multi-physics from ultraslow-to-standard-to-superdiffusion/wave dynamics.We develop a unified,fast,and stable Petrov–Galerkin spectral method for such models by employing Jacobi poly-fractonomials and Legendre polynomials as temporal and spatial basis/test functions,respectively.By defining the proper underlying distributed Sobolev spaces and their equivalent norms,we rigorously prove the well-posedness of the weak formulation,and thereby,we carry out the corresponding stability and error analysis.We finally provide several numerical simulations to study the performance and convergence of proposed scheme.
基金supported by the Ministry of Innovation and Technology,NRDI(National Research,Development and Innovation Office)under Grant No.KKP 137490its Autonomous Systems National Laboratory Program(ARNL)。
文摘The authors consider the problem of reaching consensus over a communication network via asynchronous interaction between pairs of agents.A well-known method is the linear gossip algorithm due to Tsitsiklis(1984).Extension of this,allowing the selection of a strictly stationary sequence of communicating pairs,was given in Picci and Taylor(2013).Extension of the linear gossip algorithm to directed communication networks,retaining the linear dynamics,was proposed by Cai and Ishii(2012),later extended by Silvestre,et al.(2018).A definite novelty of these algorithms is that L2-convergence with exponential rate can be established.The authors attend the above issues,extending the result of Picci and Taylor(2013)motivated by features of algorithms for directed networks.The authors present and discuss the algorithm of Silvestre,et al.(2018),together with systematic simulation results based on 5M randomly chosen parameter settings.The core of the proposed mathematical technology is a set of simple observations,presented with a tutorial aspect,by which the authors can conveniently establish various results on the almost sure convergence of products of strictly stationary sequences of matrices to a rank-1 matrix.
文摘After one year＇s delay due to the big earthquake in 2011, the Second Institute of Mathematical Statistics Asia Pacific Rim Meeting （IMS-APRM） was held in Tsukuba, Japan, in July of 2012. As a member of the Scientific Committee of the meeting, I was responsible to mobilize participants from China and to recommend invited speakers. My inexperience in fulfilling the task was easily compensated by the enthusiasm of my colleagues. More than 10 statisticians and probabilists from the mainland of China gave invited talks. In particular, Professor Zhi Geng of Peking University delivered a Distinguished Lecture. Recent progress in probability and statistics in China was well presented. When I was asked by the Editor in Chief, Professor K. -C. Chang, to compile a special issue for Frontiers of Mathematics in China, I once again turned to the speakers for help.
基金Project supported by the Doctoral Programme Science Foundation and tbe National Natural Science Foundation of China.
文摘In many lifetime studies, some of the subjects under study are censored on the righ bya prior censoring time. We observe only the censored data. It is important to estimatethe life characteristics of the subjects. Let T<sub>1</sub>, T<sub>2</sub>,…, T<sub>n</sub> be independent and identically dis-tributed nonnegative random variables with common continuous distribution funtion F
文摘Here we study the problems of local asymptotic normality of the parametric family of distri-butions and asymptotic minimax efficient estimators when the observations are subject to right censor-ing. Local asymptotic normality will be established under some mild regularity conditions. A lower bound for local asymptotic minimax risk is given with respect to a bowl-shaped loss function, and fur-thermore a necessary and sufficient condition is given in order to achieve this lower bound. Finally, we show that this lower bound can be attained by the maximum likelihood estimator in the censored case and hence it is local asymptotic minimax efficient.
基金Supported by the National Science Foundation of China under Grants No 60402011, and the National Eleven Five-Year Scientific and Technical Support Plans under Grant 2006BAH03B05.
文摘A number of researching works have shed light on the field of complex networks recently. We investigate a wide range of real-world networks and find several interesting phenomena. Firstly, almost all of these networks evolve by overlapping new small graphs on former networks. Secondly, not only the degree sequence of the mature network follows a power-law distribution, but also the distribution of the cumulative occurrence times during the growing process are revealed to have a heavy tail. Existing network evolving models do not provide interpretation to these phenomena. We suggest a model based on the team assembling mechanism, which is extracted from the growing processes of real-world networks and requires simple parameters, and produces networks exhibiting these properties observed in the present study and in previous works.
文摘We give a new way to price American options by using Samuelson’s formula. We first obtain the option price corresponding to a European option at time t, weighing it by the probability that the underlying asset takes the value S at time t. We then use Samuelson’s formula with this factor which is given by the solution of the Fokker-Planck (Kolmogorov) equation for the transition probability density. The main advantage of this approach is that we can systematically introduce the effect of macroeconomic factors. If a macroeconomic framework is given by a dynamical system in the form of a set of ordinary differential equations we only have to solve a partial differential equation for the transition probability density. In this context, we verify, for the sake of consistency, that this formula coincides with the Black-Scholes model and compare several numerical implementations.
文摘Let B be a separable real Banach space and m be a positive measure on B. In this paper, we will establish the Beurling-Deny formulae of the Dirichlet forms on L~2(B, dm).
文摘Background It is well recognized that meteorological factors have important influences on the onset and development of many kinds of diseases. The present study was undertaken to investigate the effects of the meteorological elements on admission rates of cerebral infarction patients with hypertensive nephropathy at Changchun city, Jilin Province, northeast China. Methods A total of 763 medical records of inpatients from nine hospitals at Changchun city, during a period from April 6 to April 17 in 2010, were reviewed. These patients were admitted to hospitals due to the occurrence of cerebral infarction. The hypertensive nephropathy was evidenced with certain diagnosis of essential hypertension and hypertension-related kidney injuries. The cerebral infarction was diagnosed according to the World Health Organization （Stroke） standard. All the meteorological data were from practical monitoring records in Jilin Province Meteorological Observatory. The relationships between the epidemiological prevalence of cerebral infarction and meteorological variables were analyzed using the time series models of statistics. Results Compared with admission rates before the violent change in meteorological status （April 6 to April 17, 2010）, the number of admission patients suffering from cerebral infarction remarkably peaked on April 12. Such an increase was highly correlated with heavy precipitation, elevation of daily average relative humidity, and reduction of average daily air temperature. With the betterment of the meteorological conditions on April 17, the admission rates of cerebral infarction patients dropped to the same level as the dates before snowing （April 6 to April 11）. Conclusions The meteorological changes are highly associated with the occurrence of cerebral infarction in patients with hypertensive renal injury in northeast China. This study also suggested that an intensive medical interference for those patients with hypertension-induced organ injuries is very necessary in preventing the occurrence of cerebral infarction with hypertensive nephropathy when there is a violent change in meteorological condition
基金Project supported by the Doctoral Programme Science Foundation and the National Natural Science Foundation of China.
文摘For the fixed design regression modelwhen Y, are randomly censored on the right, the estimators of unknown parameter and regression function g from censored observations are defined in the two cases .where the censored distribution is known and unknown, respectively. Moreover, the sufficient conditions under which these estimators are strongly consistent and pth (p>2) mean consistent are also established.
基金Project partially supported by the National Natural Science Foundation of China and a Postdoctoral Fellowship of the State Education Commission.
文摘A family of irreducible Markov chains on a finite state space is considered as an exponential perturbation of a reducible Markov chain. This is a generalization of the Freidlin-Wentzell theory, motivated by studies of stochastic Ising models, neural network and simulated annealing. It is shown that the metastability is a universal feature for this wide class of Markov chains. The metastable states are simply those recurrent states of the reducible Markov chain. Higher level attractors, related attractive basins and their pyramidal structure are analysed. The logarithmic asymptotics of the hitting time of various sets are estimated. The hitting time over its mean converges in law to the unit exponential distribution.
基金Project supported by China Postdoctoral Science Foundation and the National Science Foundation of China.
文摘Suppose that the patients’ survival times,Y,are random variables following the semiparametric regression model Y=Xβ+g(T)+ε,where (X,T) is a radom vector taking values in R×[0,1],β is an unknown parameter,g(·) is an unknown smooth regression function and εis the random error with zero mean and variance σ2.It is assumed that (X,T) is independent of ε.The estimators βn and gm(·) ofβ and g(·) are defined,respectively,when the observations are randomly censored on the right and the censoring distribution is unknown.Moreover,it isshown that βm is asymptotically normal and gm(·) is weak consistence with rate Op(n-1/3).
文摘For regression analysis, some useful information may have been lost when the responses are right censored. To estimate nonparametric functions, several estimates based on censored data have been proposed and their consistency and convergence rates have been studied in literature, but the optimal rates of global convergence have not been obtained yet. Because of the possible information loss, one may think that it is impossible for an estimate based on censored data to achieve the optimal rates of global convergence for nonparametric regression, which were established by Stone based on complete data. This paper constructs a regression spline estimate of a general nonparametric regression function based on right-censored response data, and proves, under some regularity conditions, that this estimate achieves the optimal rates of global convergence for nonparametric regression. Since the parameters for the nonparametric regression estimate have to be chosen based on a data driven criterion, we also obtain the asymptotic optimality of AIC, AICC, GCV, CP, and FPE criteria in the process of selecting the parameters.
基金Project supported by Doctoral Programm Foundation of Institution of Higher Education. the National Natural Science Foundation of China and 863 Programm.
文摘The closed form of the entropy production of stationary diffusion processes with bounded Nelson’s current velocity is given.The limit of the entropy productions of a sequence of reflecting diffusions is also discussed.
文摘Consider the partially linear modelY<sub>i</sub>=X<sub>i</sub><sup>τ</sup>β<sub>0</sub>+ g<sub>0</sub>（T<sub>i</sub>）+e<sub>i</sub>,where （T<sub>1</sub>, X<sub>1</sub><sup>τ</sup>, Y<sub>1</sub>）,…,（T<sub>n</sub>,X<sub>n</sub><sup>τ</sup>, Y<sub>n</sub>） are i. i. d. observations of a random （d+2）-vector （T,X<sup>τ</sup>, Y）, X=（x<sub>1</sub>,…,x<sub>d</sub>）<sup>τ</sup> is a d-vector of explanatory variables, β<sub>0</sub> is a vector of unknownparameters, T is another explanatory variable ranging over a nondegenerate compactinterval, say [0, 1],g<sub>0</sub>（·）is an unknown smooth function, and e<sub>i</sub>’s are random errors.
文摘Consider a stable AR model of two parameter spatial series {X<sub>t</sub>, t∈N<sup>2</sup>}, i. e. {X<sub>t</sub>t∈N<sup>2</sup>} is homogeneous and satisfies the following difference equationX<sub>t</sub>-sum from n=s∈【v,p] to a<sub>s</sub>X<sub>t-s</sub>=W<sub>t</sub> （t∈N<sup>2</sup>）where {W<sub>t</sub>, t∈N<sup>2</sup>} is a two parameter white noise and the notation【3, p] expresses the set of two dimentional lattice points {（k<sub>1</sub>, k<sub>2</sub>）: 0≤k<sub>1</sub>≤p<sub>1</sub>, 0≤k<sub>2</sub>≤p<sub>2</sub> but （k<sub>1</sub>, k<sub>2</sub>）≠（0, 0）}, and furthermore the two-variable polynomial1-sum from n=（s<sub>1</sub>,s<sub>2</sub>）∈【0,p] a（s<sub>1</sub>,s<sub>2</sub>） Z<sub>1</sub><sup>k</sup><sub>1</sub>Z<sub>2</sub><sup>s</sup><sub>2</sub>≠0（|Z<sub>1</sub>|≤1,|Z<sub>2</sub>|≤1）.In this paper, under frirly general conditions （it is required that {W<sub>t</sub>} Satisfies the conditions of two-parameter martingale difference, which is much weaker than supposing {W<sub>t</sub>} to be i. i. d.）, the author obtains strong consistency and asymptotic normality of the Y-W （LS） estimate of the AR parameters {a<sub>s</sub>} whenever n<sub>1</sub>n<sub>2</sub>→∞, where n<sub>1</sub> and denote the horizontal and vertical sampling width respectively.
基金Project supported by the National Natural Science Foundation of China.
文摘Suppose that (x_t,t≥0) is a stochastic process of the exponential type with P_θ(x_t∈B) =∫_B exp{θ_x - tψ(θ)}γ(t,x)V_t(dx),where θ∈Θ? (-∞,∞) and V_t is a measure. For testing the hypothesis θ≤θ_0 againstθ>θ_0, we have found a class of truncated sequential tests with probability of the first kindof error not exceeding α, the expected observation time of tests being asymptoticallyminimal as α ↓0.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10071004).
文摘The conventional method for testing hypotheses is to find an exact or asymptotic distributionof a test statistic. But when the model is complex and the sample size is small, difficulty often arises. Thispaper aims to present a method for finding maximum probability with the help of EM algorithm. For any fixedsample size, this method can be used not only to obtain an accurate test but also to check the real level ofa test which is build by large sample theory. Especially, while doing this, one needs neither the accurate norasymptotic distribution of the test statistic. So the method is easily performed and is especially useful for small samples.
