In this paper, we construct the EB estim ation for the parameter of the two-dimensional one side truncat ed distribution fam ilies using Linex loss. The convergence rate of EB estimation is given and it is shown tha...In this paper, we construct the EB estim ation for the parameter of the two-dimensional one side truncat ed distribution fam ilies using Linex loss. The convergence rate of EB estimation is given and it is shown that the proposed empirical Bayes estimaiton can be arbitrarily close to 1 under certain conditions.展开更多
A Bayesian method is used to evaluate the component safety failure model parameter of the safe arming system of an air faced missile in flight. It was proved that Bayes estimation of the model parameter is coinciden...A Bayesian method is used to evaluate the component safety failure model parameter of the safe arming system of an air faced missile in flight. It was proved that Bayes estimation of the model parameter is coincident with the physical explanation of the prior probability density distribution of the random parameter.展开更多
In present paper, the properties of the Bayes Shrinkage estimator is studied for the measure of dispersion of an inverse Gaussian model under the Minimax estimation criteria.
Under square loss, this paper constructs the empirical Bayes（EB） estimation for the parameter of normal distribution which has both asymptotic optimality and admissibility. Moreover, the convergence rate of the EB e...Under square loss, this paper constructs the empirical Bayes（EB） estimation for the parameter of normal distribution which has both asymptotic optimality and admissibility. Moreover, the convergence rate of the EB estimation obtained is proved to be O（n^-1）.展开更多
The empirical Bayes estimation for parameters of the one-side truncated distribution family with convergence rate which can close to 1 arbitrarily is investigated using NA samples and an exam-ple that satisfies the co...The empirical Bayes estimation for parameters of the one-side truncated distribution family with convergence rate which can close to 1 arbitrarily is investigated using NA samples and an exam-ple that satisfies the conditions of theorem is given.展开更多
In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares...In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.展开更多
This paper presents the Bayes estimation and empirical Bayes estimation of causal effects in a counterfactual model. It also gives three kinds of prior distribution of the assumptions of replaceability. The experiment...This paper presents the Bayes estimation and empirical Bayes estimation of causal effects in a counterfactual model. It also gives three kinds of prior distribution of the assumptions of replaceability. The experiment shows that empirical Bayes estimation is better than other estimations when not knowing which assumption is true.展开更多
In this paper, the Bayes estimator of the error variance is derived in a linear regression model, and the parametric empirical Bayes estimator （PEBE） is constructed. The superiority of the PEBE over the least square...In this paper, the Bayes estimator of the error variance is derived in a linear regression model, and the parametric empirical Bayes estimator （PEBE） is constructed. The superiority of the PEBE over the least squares estimator （LSE） is investigated under the mean square error （MSE） criterion. Finally, some simulation results for the PEBE are obtained.展开更多
In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard n...In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.展开更多
For the multi-parameter discrete exponential family,we construct an empirical Bayes(EB)estimator of the vector-valued parameterθ.under some conditions,this estimator is proved to be asymptotically optimal.
In this paper we propose an absolute error loss EB estimator for parameter of one-side truncation distribution families. Under some conditions we have proved that the convergence rates of its Bayes risk is o, where 0&...In this paper we propose an absolute error loss EB estimator for parameter of one-side truncation distribution families. Under some conditions we have proved that the convergence rates of its Bayes risk is o, where 0<λ,r≤1,Mn≤lnln n (for large n),Mn→∞ as n→∞.展开更多
In this paper,we propose a new image fusion algorithm based on two-dimensional Scale-Mixing Complex Wavelet Transform(2D-SMCWT).The fusion of the detail 2D-SMCWT cofficients is performed via a Bayesian Maximum a Poste...In this paper,we propose a new image fusion algorithm based on two-dimensional Scale-Mixing Complex Wavelet Transform(2D-SMCWT).The fusion of the detail 2D-SMCWT cofficients is performed via a Bayesian Maximum a Posteriori(MAP)approach by considering a trivariate statistical model for the local neighboring of 2D-SMCWT coefficients.For the approx imation coefficients,a new fusion rule based on the Principal Component Analysis(PCA)is applied.We conduct several experiments using three different groups of multimodal medical images to evaluate the performance of the proposed method.The obt ained results prove the superiority of the proposed method over the state of the art fusion methods in terms of visual quality and several commonly used metrics.Robustness of the proposed method is further tested against different types of noise.The plots of fusion met rics establish the accuracy of the proposed fusion method.展开更多
Consider the one-way analysis of variance (ANOVA) model Yij=μ+αi+∈ij,i=1,…,a; j = 1,…,b, ∈ij～N(0, σ2). By using the kernel estimation of multivariate density function and its partial derivatives and making use...Consider the one-way analysis of variance (ANOVA) model Yij=μ+αi+∈ij,i=1,…,a; j = 1,…,b, ∈ij～N(0, σ2). By using the kernel estimation of multivariate density function and its partial derivatives and making use of the estimators of nuisance parameters μ and σ2, we construct the empirical Bayes (EB) estimators of parameter vector α = (α1,…，αa)T. Under the existence condition of the second order moment on prior distribution, we obtain their asymptotic optimality.展开更多
The estimation of the functionθ=exp{αμ+bσ2} of parameters (μ,σ2) in normal distribution N(μ,σ2) is discussed. And when the prior distributions ofμandσ2 are independent, under the loss function L(θ,δ)=(θ-1...The estimation of the functionθ=exp{αμ+bσ2} of parameters (μ,σ2) in normal distribution N(μ,σ2) is discussed. And when the prior distributions ofμandσ2 are independent, under the loss function L(θ,δ)=(θ-1×δ-1)2, the Bayesian estimation and the existence and computing method on minimax estimation are deeply discussed.展开更多
Residual life estimation is essential for reliability engineering. Traditional methods may experience difficulties in estimating the residual life of products with high reliability, long life, and small sample. The Ba...Residual life estimation is essential for reliability engineering. Traditional methods may experience difficulties in estimating the residual life of products with high reliability, long life, and small sample. The Bayes model provides a feasible solution and can be a useful tool for fusing multisource information. In this study, a Bayes model is proposed to estimate the residual life of products by fusing expert knowledge, degradation data, and lifetime data. The linear Wiener process is used to model degradation data, whereas lifetime data are described via the inverse Gaussian distribution. Therefore, the joint maximum likelihood(ML) function can be obtained by combining lifetime and degradation data. Expert knowledge is used according to the maximum entropy method to determine the prior distributions of parameters, thereby making this work different from existing studies that use non-informative prior. The discussion and analysis of different types of expert knowledge also distinguish our research from others. Expert knowledge can be classified into three categories according to practical engineering.Methods for determining prior distribution by using the aforementioned three types of data are presented. The Markov chain Monte Carlo is applied to obtain samples of the parameters and to estimate the residual life of products due to the complexity of the joint ML function and the posterior distribution of parameters. Finally, a numerical example is presented. The effectiveness and practicability of the proposed method are validated by comparing it with residual life estimation that uses non-informative prior.Then, its accuracy and correctness are proven via simulation experiments.展开更多
We present Bayes estimators, highest posterior density (HPD) intervals, and maximum likelihood estimators (MLEs), for the Maxwell failure distribution based on Type II censored data, i.e. using the first r lifetimes f...We present Bayes estimators, highest posterior density (HPD) intervals, and maximum likelihood estimators (MLEs), for the Maxwell failure distribution based on Type II censored data, i.e. using the first r lifetimes from a group of n components under test. Reliability/Hazard function estimates, Bayes predictive distributions and highest posterior density prediction intervals for a future observation are also considered. Two data examples and a Monte Carlo simulation study are used to illustrate the results and to compare the performances of the different methods.展开更多
A Bayesian estimator with informative prior distributions （a multi-normal and an inverted gamma distribution）, adequate to displacement estimation at dam displacement monitoring networks, is presented. The hyper-par...A Bayesian estimator with informative prior distributions （a multi-normal and an inverted gamma distribution）, adequate to displacement estimation at dam displacement monitoring networks, is presented. The hyper-parameters of the prior distributions are obtained by Bayesian empirical methods with non-informative meta-priors. The performances of the Bayes estimator and the classical generalized lest squares estimator are compared using two measurements of the horizontal monitoring network of a concrete gravity dam： the Penha Garcia dam （Portugal）. In order to test the robustness of the two estimators, a gross error is added to one of the measured horizontal directions： the Bayes estimator proves to be significantly more robust than the classic maximum likelihood estimator.展开更多
We consider the problem of population estimation using capture-recapture data, where capture probabilities can vary between sampling occasions and behavioural responses. The original model is not identifiable without ...We consider the problem of population estimation using capture-recapture data, where capture probabilities can vary between sampling occasions and behavioural responses. The original model is not identifiable without further restrictions. The novelty of this article is to expand the current research practice by developing a hierarchical Bayesian approach with the assumption that the odds of recapture bears a constant relationship to the odds of initial capture. A real-data example of deer mice population is given to illustrate the proposed method. Three simulation studies are developed to inspect the performance of the proposed Bayesian estimates. Compared with the maximum likelihood estimates discussed in Chao et al. (2000), the hierarchical Bayesian estimate provides reasonably better population estimation with less mean square error;moreover, it is sturdy to underline relationship between the initial and re-capture probabilities. The sensitivity study shows that the proposed Bayesian approach is robust to the choice of hyper-parameters. The third simulation study reveals that both relative bias and relative RMSE approach zero as population size increases. A R-package is developed and used in both data example and simulation.展开更多
The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0...The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0 is considered. Formulas that determine the greatest value of mean square error and the minimax estimation for the functional are proposed for the given class of admissible processes. It is shown that one-sided moving average stationary sequence gives the greatest value of the mean square error.展开更多
文摘In this paper, we construct the EB estim ation for the parameter of the two-dimensional one side truncat ed distribution fam ilies using Linex loss. The convergence rate of EB estimation is given and it is shown that the proposed empirical Bayes estimaiton can be arbitrarily close to 1 under certain conditions.
文摘A Bayesian method is used to evaluate the component safety failure model parameter of the safe arming system of an air faced missile in flight. It was proved that Bayes estimation of the model parameter is coincident with the physical explanation of the prior probability density distribution of the random parameter.
文摘In present paper, the properties of the Bayes Shrinkage estimator is studied for the measure of dispersion of an inverse Gaussian model under the Minimax estimation criteria.
基金Supported by the Natural Science Foundation of China(70471057)Supported by the Natural Science Foundation of Education Department of Shaanxi Province(03JK065)
文摘Under square loss, this paper constructs the empirical Bayes（EB） estimation for the parameter of normal distribution which has both asymptotic optimality and admissibility. Moreover, the convergence rate of the EB estimation obtained is proved to be O（n^-1）.
文摘The empirical Bayes estimation for parameters of the one-side truncated distribution family with convergence rate which can close to 1 arbitrarily is investigated using NA samples and an exam-ple that satisfies the conditions of theorem is given.
基金the Knowledge Innovation Program of the Chinese Academy of Sciences(KJCX3-SYW-S02)the Youth Foundation of USTC
文摘In this article,the empirical Bayes（EB）estimators are constructed for the estimable functions of the parameters in partitioned normal linear model.The superiorities of the EB estimators over ordinary least-squares（LS）estimator are investigated under mean square error matrix（MSEM）criterion.
文摘This paper presents the Bayes estimation and empirical Bayes estimation of causal effects in a counterfactual model. It also gives three kinds of prior distribution of the assumptions of replaceability. The experiment shows that empirical Bayes estimation is better than other estimations when not knowing which assumption is true.
文摘In this paper, the Bayes estimator of the error variance is derived in a linear regression model, and the parametric empirical Bayes estimator （PEBE） is constructed. The superiority of the PEBE over the least squares estimator （LSE） is investigated under the mean square error （MSE） criterion. Finally, some simulation results for the PEBE are obtained.
文摘In this paper we consider the empirical Bayes (EB) estimation problem for estimable function of regression coefficient in a multiple linear regression model Y=Xβ+e. where e with given β has a multivariate standard normal distribution. We get the EB estimators by using kernel estimation of multivariate density function and its first order partial derivatives. It is shown that the convergence rates of the EB estimators are under the condition where an integer k > 1 . is an arbitrary small number and m is the dimension of the vector Y.
文摘For the multi-parameter discrete exponential family,we construct an empirical Bayes(EB)estimator of the vector-valued parameterθ.under some conditions,this estimator is proved to be asymptotically optimal.
文摘In this paper we propose an absolute error loss EB estimator for parameter of one-side truncation distribution families. Under some conditions we have proved that the convergence rates of its Bayes risk is o, where 0<λ,r≤1,Mn≤lnln n (for large n),Mn→∞ as n→∞.
文摘In this paper,we propose a new image fusion algorithm based on two-dimensional Scale-Mixing Complex Wavelet Transform(2D-SMCWT).The fusion of the detail 2D-SMCWT cofficients is performed via a Bayesian Maximum a Posteriori(MAP)approach by considering a trivariate statistical model for the local neighboring of 2D-SMCWT coefficients.For the approx imation coefficients,a new fusion rule based on the Principal Component Analysis(PCA)is applied.We conduct several experiments using three different groups of multimodal medical images to evaluate the performance of the proposed method.The obt ained results prove the superiority of the proposed method over the state of the art fusion methods in terms of visual quality and several commonly used metrics.Robustness of the proposed method is further tested against different types of noise.The plots of fusion met rics establish the accuracy of the proposed fusion method.
文摘Consider the one-way analysis of variance (ANOVA) model Yij=μ+αi+∈ij,i=1,…,a; j = 1,…,b, ∈ij～N(0, σ2). By using the kernel estimation of multivariate density function and its partial derivatives and making use of the estimators of nuisance parameters μ and σ2, we construct the empirical Bayes (EB) estimators of parameter vector α = (α1,…，αa)T. Under the existence condition of the second order moment on prior distribution, we obtain their asymptotic optimality.
文摘The estimation of the functionθ=exp{αμ+bσ2} of parameters (μ,σ2) in normal distribution N(μ,σ2) is discussed. And when the prior distributions ofμandσ2 are independent, under the loss function L(θ,δ)=(θ-1×δ-1)2, the Bayesian estimation and the existence and computing method on minimax estimation are deeply discussed.
基金funded by the National Natural Science Foundation of China(Grant No.61573370.)
文摘Residual life estimation is essential for reliability engineering. Traditional methods may experience difficulties in estimating the residual life of products with high reliability, long life, and small sample. The Bayes model provides a feasible solution and can be a useful tool for fusing multisource information. In this study, a Bayes model is proposed to estimate the residual life of products by fusing expert knowledge, degradation data, and lifetime data. The linear Wiener process is used to model degradation data, whereas lifetime data are described via the inverse Gaussian distribution. Therefore, the joint maximum likelihood(ML) function can be obtained by combining lifetime and degradation data. Expert knowledge is used according to the maximum entropy method to determine the prior distributions of parameters, thereby making this work different from existing studies that use non-informative prior. The discussion and analysis of different types of expert knowledge also distinguish our research from others. Expert knowledge can be classified into three categories according to practical engineering.Methods for determining prior distribution by using the aforementioned three types of data are presented. The Markov chain Monte Carlo is applied to obtain samples of the parameters and to estimate the residual life of products due to the complexity of the joint ML function and the posterior distribution of parameters. Finally, a numerical example is presented. The effectiveness and practicability of the proposed method are validated by comparing it with residual life estimation that uses non-informative prior.Then, its accuracy and correctness are proven via simulation experiments.
文摘We present Bayes estimators, highest posterior density (HPD) intervals, and maximum likelihood estimators (MLEs), for the Maxwell failure distribution based on Type II censored data, i.e. using the first r lifetimes from a group of n components under test. Reliability/Hazard function estimates, Bayes predictive distributions and highest posterior density prediction intervals for a future observation are also considered. Two data examples and a Monte Carlo simulation study are used to illustrate the results and to compare the performances of the different methods.
文摘A Bayesian estimator with informative prior distributions （a multi-normal and an inverted gamma distribution）, adequate to displacement estimation at dam displacement monitoring networks, is presented. The hyper-parameters of the prior distributions are obtained by Bayesian empirical methods with non-informative meta-priors. The performances of the Bayes estimator and the classical generalized lest squares estimator are compared using two measurements of the horizontal monitoring network of a concrete gravity dam： the Penha Garcia dam （Portugal）. In order to test the robustness of the two estimators, a gross error is added to one of the measured horizontal directions： the Bayes estimator proves to be significantly more robust than the classic maximum likelihood estimator.
文摘We consider the problem of population estimation using capture-recapture data, where capture probabilities can vary between sampling occasions and behavioural responses. The original model is not identifiable without further restrictions. The novelty of this article is to expand the current research practice by developing a hierarchical Bayesian approach with the assumption that the odds of recapture bears a constant relationship to the odds of initial capture. A real-data example of deer mice population is given to illustrate the proposed method. Three simulation studies are developed to inspect the performance of the proposed Bayesian estimates. Compared with the maximum likelihood estimates discussed in Chao et al. (2000), the hierarchical Bayesian estimate provides reasonably better population estimation with less mean square error;moreover, it is sturdy to underline relationship between the initial and re-capture probabilities. The sensitivity study shows that the proposed Bayesian approach is robust to the choice of hyper-parameters. The third simulation study reveals that both relative bias and relative RMSE approach zero as population size increases. A R-package is developed and used in both data example and simulation.
文摘The problem of optimal linear estimation of the functional Aξ =10^∞a（t）ζ（（t）dt depending on the unknown values of periodically correlated stochastic process ζ（t） from observations of this process for t 〈 0 is considered. Formulas that determine the greatest value of mean square error and the minimax estimation for the functional are proposed for the given class of admissible processes. It is shown that one-sided moving average stationary sequence gives the greatest value of the mean square error.
