The Superiority of Bayes Estimators in a Multivariate Linear Model with Respect to Normal-Inverse Wishart Prior

In this paper, the multivariate linear model Y = XB＋e, e ～ Nm×k（0, ImΣ） is considered from the Bayes perspective. Under the normal-inverse Wishart prior for （BΣ）, the Bayes estimators are derived. The superiority of the Bayes estimators of B and Σ over the least squares estimators under the criteria of Bayes mean squared error （BMSE） and Bayes mean squared error matrix （BMSEM） is shown. In addition, the Pitman Closeness （PC） criterion is also included to investigate the superiority of the Bayes estimator of B.

Empirical Bayes Absolute Error Loss Estimation for Parameter of One-Side Truncation Distribution Families

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→∞.

Empirical Bayes Estimation for the Parameter of Two-dimen sional One-side Truncated Distribution Families with Linex Loss

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.

THE SUPERIORITY OF EMPIRICAL BAYES ESTIMATION OF PARAMETERS IN PARTITIONED NORMAL LINEAR MODEL

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.

PARAMETER IDENTIFICATION OF DYNAMIC MODELS USING A BAYES APPROACH

The Bayesian method of statistical analysis has been applied to the parameter identification problem. A method is presented to identify parameters of dynamic models with the Bayes estimators of measurement frequencies. This is based on the solution of an inverse generalized evaluate problem. The stochastic nature of test data is considered and a normal distribution is used for the measurement frequencies. An additional feature is that the engineer's confidence in the measurement frequencies is quantified and incorporated into the identification procedure. A numerical example demonstrates the efficiency of the method.

Estimator of Scale Parameter in a Subclass of the Exponential Family under Symmetric Entropy Loss

In this paper we investigate the estimator for the rth power of the scale parameter in a class of exponential family under symmetric entropy loss L（θ, δ） = v（θ/δ ＋ δ/θ - 2）. An exact form of the minimum risk equivariant estimator under symmetric entropy loss is given, and the minimaxity of the minimum risk equivariant estimator is proved. The results with regard to admissibility and inadmissibility of a class of linear estimators of the form cT（X） ＋ d are given, where T（X） Gamma（v, θ）.

Evaluations of Chris-Jerry Data Using Generalized Progressive Hybrid Strategy and Its Engineering Applications

A new one-parameter Chris-Jerry distribution,created by mixing exponential and gamma distributions,is discussed in this article in the presence of incomplete lifetime data.We examine a novel generalized progressively hybrid censoring technique that ensures the experiment ends at a predefined period when the model of the test participants has a Chris-Jerry(CJ)distribution.When the indicated censored data is present,Bayes and likelihood estimations are used to explore the CJ parameter and reliability indices,including the hazard rate and reliability functions.We acquire the estimated asymptotic and credible confidence intervals of each unknown quantity.Additionally,via the squared-error loss,the Bayes’estimators are obtained using gamma prior.The Bayes estimators cannot be expressed theoretically since the likelihood density is created in a complex manner;nonetheless,Markov-chain Monte Carlo techniques can be used to evaluate them.The effectiveness of the investigated estimations is assessed,and some recommendations are given using Monte Carlo results.Ultimately,an analysis of two engineering applications,such as mechanical equipment and ball bearing data sets,shows the applicability of the proposed approaches that may be used in real-world settings.

Bayesian Estimation in Dam Monitoring Networks

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.

Bayes Estimation of Parameter for the Safety Component Failure Model of the Safe Arming System of Missile

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.

Bayesian Estimation and Prediction for the Maxwell Failure Distribution Based on Type II Censored Data

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.

EMPIRICAL BAYES ESTIMATION FOR ESTIMABLE FUNCTION OF REGRESSION COEFFICIENT IN A MULTIPLE LINEAR REGRESSION MODEL

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.

A novel image fusion algorithm based on 2D scale-mixing complex wavelet transform and Bayesian MAP estimation for multimodal medical images

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.

ASYMPTOTICALLY OPTIMAL EMPIRICAL BAYES ESTIMATION FOR THE PARAMETERS OF MULTI－PARAMETER DISCRETE EXPONENTIAL FAMILY

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.

Asymptotically Optimal and Admissible Empirical Bayes Estimation of Normal Parameter

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）.

A Comparison of Four Methods of Estimating the Scale Parameter for the Exponential Distribution

In this paper, the estimators of the scale parameter of the exponential distribution obtained by applying four methods, using complete data, are critically examined and compared. These methods are the Maximum Likelihood Estimator (MLE), the Square-Error Loss Function (BSE), the Entropy Loss Function (BEN) and the Composite LINEX Loss Function (BCL). The performance of these four methods was compared based on three criteria: the Mean Square Error (MSE), the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC). Using Monte Carlo simulation based on relevant samples, the comparisons in this study suggest that the Bayesian method is better than the maximum likelihood estimator with respect to the estimation of the parameter that offers the smallest values of MSE, AIC, and BIC. Confidence intervals were then assessed to test the performance of the methods by comparing the 95% CI and average lengths (AL) for all estimation methods, showing that the Bayesian methods still offer the best performance in terms of generating the smallest ALs.

Parameter Estimations in BurrⅫ Model Using Masked Data

We consider a series system of two independent and non-identical components which have different BurrⅫ distributed lifetime.The maximum likelihood and Bayes estimators of the parameters of the system＇s components are obtained based on masked system life test data.The conclusion is that the Bayes estimates are better than the maximum likelihood estimates in the sense of having smaller mean squared errors.

The Superiorities of Bayes Linear Unbiased Estimator in Multivariate Linear Models

In this article, the Bayes linear unbiased estimator （BALUE） of parameters is derived for the multivariate linear models. The superiorities of the BALUE over the least square estimator （LSE） is studied in terms of the mean square error matrix （MSEM） criterion and Bayesian Pitman closeness （PC） criterion.

Inference for Gompertz distribution under records

The parameter estimation is considered for the Gompertz distribution under frequensitst and Bayes approaches when records are available.Maximum likelihood estimators,exact and approximate confidence intervals are developed for the model parameters,and Bayes estimators of reliability performances are obtained under different losses based on a mixture of continuous and discrete priors.To investigate the performance of the proposed estimators,a record simulation algorithm is provided and a numerical study is presented by using Monte-Carlo simulation.

Statistical Inference for the Parameter of Pareto Distribution Based on Progressively Type-I Interval Censored Sample

In this paper, the estimation of parameters based on a progressively typeI interval censored sample from a Pareto distribution is studied. Different methods of estimation are discussed, which include mid-point approximation estimator, the maximum likelihood estimator and moment estimator. The estimation procedures are discussed in details and compared via Monte Carlo simulations in terms of their biases.

Bayes Estimation of Causal Effect for a Counterfactural Model

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.