Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） ...Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） is obtained in QLNM. In an important case, this rate is O（n-^1/2（loglogn）^1/2）, which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.展开更多
A modified Bates and Watts geometric framework is proposed for quasi\|likelihood nonlinear models in Euclidean inner product space.Based on the modified geometric framework,some asymptotic inference in terms of curvat...A modified Bates and Watts geometric framework is proposed for quasi\|likelihood nonlinear models in Euclidean inner product space.Based on the modified geometric framework,some asymptotic inference in terms of curvatures for quasi\|likelihood nonlinear models is studied.Several previous results for nonlinear regression models and exponential family nonlinear models etc.are extended to quasi\|likelihood nonlinear models.展开更多
This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator （MQLE） in quasi-likelihood nonlinear models （QLNM） w...This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator （MQLE） in quasi-likelihood nonlinear models （QLNM） with random regressors. The asymptotic results of generalized linear models （GLM） with random regressors are generalized to QLNM with random regressors.展开更多
This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation （MQLE） in quasi-likelihood nonlinear models ...This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation （MQLE） in quasi-likelihood nonlinear models （QLNM）. Our results may be regarded as a further generalization of the relevant results in Ref. [4].展开更多
In a generalized linear model with q x 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ZiZ'i,...In a generalized linear model with q x 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ZiZ'i,the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.展开更多
In a generalized linear model with q×1 responses, bounded and fixed p×q regressors zi and general link function, under the most general assumption on the minimum eigenvalue of ∑in=1 ZiZi', the moment co...In a generalized linear model with q×1 responses, bounded and fixed p×q regressors zi and general link function, under the most general assumption on the minimum eigenvalue of ∑in=1 ZiZi', the moment condition on responses as weak as possible and other mild regular conditions, we prove that with probability one, the quasi-likelihood equation has a solution βn for all large sample size n, which converges to the true regression parameter β0. This result is an essential improvement over the relevant results in literature.展开更多
In generalized linear models with fixed design, under the assumption λ↑_n→∞ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator ^↑βn, which is the root of the quasi-li...In generalized linear models with fixed design, under the assumption λ↑_n→∞ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator ^↑βn, which is the root of the quasi-likelihood equation with natural link function ∑i=1^n Xi（yi -μ（Xi′β）） = 0, is obtained, where λ↑_n denotes the minimum eigenvalue of ∑i=1^nXiXi′, Xi are bounded p × q regressors, and yi are q × 1 responses.展开更多
In this paper, for the generalized linear models （GLMs） with diverging number of covariates, the asymptotic properties of maximum quasi-likelihood estimators （MQLEs） under some regular conditions are developed. Th...In this paper, for the generalized linear models （GLMs） with diverging number of covariates, the asymptotic properties of maximum quasi-likelihood estimators （MQLEs） under some regular conditions are developed. The existence, weak convergence and the rate of convergence and asymptotic normality of linear combination of MQLEs and asymptotic distribution of single linear hypothesis teststatistics are presented. The results are illustrated by Monte-Carlo simulations.展开更多
In this paper, the estimation of average treatment effects is considered when we have the model information of the conditional mean and conditional variance for the responses given the covariates. The quasi-likelihood...In this paper, the estimation of average treatment effects is considered when we have the model information of the conditional mean and conditional variance for the responses given the covariates. The quasi-likelihood method adapted to treatment effects data is developed to estimate the parameters in the conditional mean and conditional variance models. Based on the model information, we define three estimators by imputation, regression and inverse probability weighted methods. All the estimators are shown asymptotically normal. Our simulation results show that by using the model information, the substantial efficiency gains are obtained which are comparable with the existing estimators.展开更多
In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem...In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem, the new quasi-likelihood proposed in this paper is based mainly on a linearly iterative process of some unbiased estimating functions.Some finite sample properties and asymptotic behaviours for this new quasi-likelihood are investigated. These results show that the new quasi-likelihood for parameter of interest is E-sufficient, iteratively efficient and approximately efficient. Some examples are given to illustrate the theoretical results.展开更多
Let B^(H)={B_(t)^(H),t≥0}be a fractional Brownian motion with Hurst index 0<H<1,and let B={B_(t),t≥0}be an independent Brownian motion.In this study,we investigate the parameter estimation of a mixed fractiona...Let B^(H)={B_(t)^(H),t≥0}be a fractional Brownian motion with Hurst index 0<H<1,and let B={B_(t),t≥0}be an independent Brownian motion.In this study,we investigate the parameter estimation of a mixed fractional Black-Scholes modelS_(t)^(H)=S_(0)^(H)+μ∫_(0)^(t)S_(s)^(H)ds+σ∫_(0)^(t)S_(s)^(H)d(B_(s)+B_(s)^(H)),whereσ>0,μ∈Rare two unknown parameters.Using quasi-likelihood estimation,when the system is observed at some discrete time instants{t_(i)=ih,i=0,1,2,…,n},we give estimations of the parametersμandσprovided h=h(n)→0 nh→∞and h^(1+γ)n→1for someγ>0,as n→∞.We present the asymptotic normality of the estimators based on the velocity of nh^(1+γ)-1 tending to zero as n tends to infinity.Finally,we perform numerical calculus and simulations using factual data from the stock market to verify the effectiveness of the established estimators.展开更多
基金Supported by the National Natural Sciences Foundation of China (10761011)Mathematical Tianyuan Fund of National Natural Science Fundation of China(10626048)
文摘Quasi-likelihood nonlinear models （QLNM） include generalized linear models as a special case. Under some regularity conditions, the rate of the strong consistency of the maximum quasi-likelihood estimation （MQLE） is obtained in QLNM. In an important case, this rate is O（n-^1/2（loglogn）^1/2）, which is just the rate of LIL of partial sums for i.i.d variables, and thus cannot be improved anymore.
基金The project supported by NSFC!(19631040)NSFJ!(BK99002)
文摘A modified Bates and Watts geometric framework is proposed for quasi\|likelihood nonlinear models in Euclidean inner product space.Based on the modified geometric framework,some asymptotic inference in terms of curvatures for quasi\|likelihood nonlinear models is studied.Several previous results for nonlinear regression models and exponential family nonlinear models etc.are extended to quasi\|likelihood nonlinear models.
基金Supported by National Natural Science Foundation of China (No. 10761011,10671139,10901135)Natural Science Foundation of Yunnan Province(No. 2008CD081)Special Foundation for Middle and Young Excellent Teachers of Yunnan University
文摘This paper proposes some regularity conditions, which result in the existence, strong consistency and asymptotic normality of maximum quasi-likelihood estimator （MQLE） in quasi-likelihood nonlinear models （QLNM） with random regressors. The asymptotic results of generalized linear models （GLM） with random regressors are generalized to QLNM with random regressors.
基金the Natural Science Foundation of Yunnan University （No. 2005Z007C） the Scientific Research Fund of Yunnan Provincial Education Department （No. 5Y0062A）+1 种基金 Mathematical Tianyuan Fund of National Natural Science Foundation of China （No. 10626048） Special Foundation for Middle and Young Excellent Teachers of Yunnan University.
文摘This paper proposes some regularity conditions. On the basis of the proposed regularity conditions, we show the strong consistency of maximum quasi-likelihood estimation （MQLE） in quasi-likelihood nonlinear models （QLNM）. Our results may be regarded as a further generalization of the relevant results in Ref. [4].
基金supported by the National Natural Science Foundation of China(Grant No.10471136)Ph.D.Program Foundation of Ministry of Education of China and Special Foundation of the Chinese Academy of Science and USTC.
文摘In a generalized linear model with q x 1 responses, the bounded and fixed (or adaptive) p × q regressors Zi and the general link function, under the most general assumption on the minimum eigenvalue of ZiZ'i,the moment condition on responses as weak as possible and the other mild regular conditions, we prove that the maximum quasi-likelihood estimates for the regression parameter vector are asymptotically normal and strongly consistent.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.10171094&10471136)Ph.D.Program Foundation of Ministry of Education of ChinaSpecial Foundations of the Chinese Academy of Science and USTC.
文摘In a generalized linear model with q×1 responses, bounded and fixed p×q regressors zi and general link function, under the most general assumption on the minimum eigenvalue of ∑in=1 ZiZi', the moment condition on responses as weak as possible and other mild regular conditions, we prove that with probability one, the quasi-likelihood equation has a solution βn for all large sample size n, which converges to the true regression parameter β0. This result is an essential improvement over the relevant results in literature.
基金the National Natural Science Foundation of China under Grant Nos.10171094,10571001,and 30572285the Foundation of Nanjing Normal University under Grant No.2005101XGQ2B84+1 种基金the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No.07KJD110093the Foundation of Anhui University under Grant No.02203105
文摘In generalized linear models with fixed design, under the assumption λ↑_n→∞ and other regularity conditions, the asymptotic normality of maximum quasi-likelihood estimator ^↑βn, which is the root of the quasi-likelihood equation with natural link function ∑i=1^n Xi（yi -μ（Xi′β）） = 0, is obtained, where λ↑_n denotes the minimum eigenvalue of ∑i=1^nXiXi′, Xi are bounded p × q regressors, and yi are q × 1 responses.
基金supported by Major Programm of Natural Science Foundation of China under Grant No.71690242the Natural Science Foundation of China under Grant No.11471252the National Social Science Fund of China under Grant No.18BTJ040
文摘In this paper, for the generalized linear models （GLMs） with diverging number of covariates, the asymptotic properties of maximum quasi-likelihood estimators （MQLEs） under some regular conditions are developed. The existence, weak convergence and the rate of convergence and asymptotic normality of linear combination of MQLEs and asymptotic distribution of single linear hypothesis teststatistics are presented. The results are illustrated by Monte-Carlo simulations.
文摘In this paper, the estimation of average treatment effects is considered when we have the model information of the conditional mean and conditional variance for the responses given the covariates. The quasi-likelihood method adapted to treatment effects data is developed to estimate the parameters in the conditional mean and conditional variance models. Based on the model information, we define three estimators by imputation, regression and inverse probability weighted methods. All the estimators are shown asymptotically normal. Our simulation results show that by using the model information, the substantial efficiency gains are obtained which are comparable with the existing estimators.
基金Project supported by the National Natural Science Foundation of China (No.10371059, No.10171051).
文摘In the seemingly unrelated regression systems, the existing quasi-likelihood is always involved in the difficult problem of calculating inverse of a high order matrix specially for large systems. To avoid this problem, the new quasi-likelihood proposed in this paper is based mainly on a linearly iterative process of some unbiased estimating functions.Some finite sample properties and asymptotic behaviours for this new quasi-likelihood are investigated. These results show that the new quasi-likelihood for parameter of interest is E-sufficient, iteratively efficient and approximately efficient. Some examples are given to illustrate the theoretical results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11971101 and 12171081)Shanghai Natural Science Foundation(Grant No.24ZR1402900).
文摘Let B^(H)={B_(t)^(H),t≥0}be a fractional Brownian motion with Hurst index 0<H<1,and let B={B_(t),t≥0}be an independent Brownian motion.In this study,we investigate the parameter estimation of a mixed fractional Black-Scholes modelS_(t)^(H)=S_(0)^(H)+μ∫_(0)^(t)S_(s)^(H)ds+σ∫_(0)^(t)S_(s)^(H)d(B_(s)+B_(s)^(H)),whereσ>0,μ∈Rare two unknown parameters.Using quasi-likelihood estimation,when the system is observed at some discrete time instants{t_(i)=ih,i=0,1,2,…,n},we give estimations of the parametersμandσprovided h=h(n)→0 nh→∞and h^(1+γ)n→1for someγ>0,as n→∞.We present the asymptotic normality of the estimators based on the velocity of nh^(1+γ)-1 tending to zero as n tends to infinity.Finally,we perform numerical calculus and simulations using factual data from the stock market to verify the effectiveness of the established estimators.
