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.     

The empirical bayes rules with floating optimal sample size for exponential conditional distributions

Summary We consider the empirical Bayes solution in such a situation where the sample size is successively determined by a rule which includes the Bayes risks and the observation costs. The empirical Bayes floating optimal sample size depends on current as well as on previous information assumed to be collected from earlier performances of similar decisions. The sampling is done from an exponential conditional distribution, with a single parameter. The proofs, which show the asymptotic optimality of the empirical Bayes solution, are presented for a hypotheses-testing problem. A straight generalization to a multiple decision problem is also given.     

Admissible estimators of binomial probability and the inverse bayes rule map

Explicit formulae for prior distribution moments through values of the Bayes estimator of binomial probability are obtained. These are used to derive a new admissibility criterion.Research supported by National Science Foundation Grants #DMS-8702620 and #DMS-8802359.     

刻度指数族参数的经验Bayes检验函数收敛速度的改进

在加权线性损失下导出了刻度指数族中参数单调的Bayes检验函数,利用同分布负相协(NA)样本情形概率密度函数及其导数的核估计构造了经验Bayes(EB)检验函数,获得了EB检验函数的收敛速度.在适当的条件下,这一收敛速度可任意接近O(n~(-1)),改进了文献中已有的结果.对同分布正相协(PA)样本和独立同分布(iid)样本情形,亦可获得类似结论.最后给出了一个满足文中主要结果的例子.     

Minimax estimators of the multinormal mean: Autoregressive priors

Empirical Bayes estimators are given for the mean of a k-dimensional normal distribution, k ≥ 3. We assume that y ～ N_k(θ, V₁), V₁ = diag(v_i), v_i known (i = 1, 2,…, k); also, θ ～ N_k(0, V₂) ? V₂ defined by one or more unknown parameters. Of particular interest is V₂ generated by an autoregressive process. A recent result of Efron and Morris is used to obtain necessary and sufficient conditions for the minimaxity of our estimators. Practical sufficient conditions (for minimaxity) are obtained by exploiting the structure of V₂. Another result shows that our estimators have good Bayesian properties. Estimates of the exact size of Pearson's chi-square test are given in an example; the autoregressive prior is very natural in this situation.     

Assessing the lifetime performance index of Rayleigh products based on the Bayesian estimation under progressive type II right censored samples

Lifetime performance assessment is important in service (or manufacturing) industries. Hence, lifetime performance index C_L is used to measure the potential and performance of a process, where L is the lower specification limit. In this paper, assuming the conjugate prior distribution and squared-error loss function, this study constructs a Bayes estimator under the Rayleigh distribution with the progressive type II right censored sample. The Bayes estimator of C_L is then utilized to develop a credible interval in the condition of known L. Moreover, we also propose a Bayesian test to assess the lifetime performance of products. Finally, we give two examples and the Monte Carlo simulation to assess the behavior of the lifetime performance index C_L. Moreover, the purchasers can then employ the credible interval and the Bayesian test to determine whether the product performance adheres to the required level.     

负相伴样本情形连续型单参数指数族参数的经验Bayes检验问题

在加权"线性损失"下讨论了负相伴样本情形连续型单参数指数族参数的经验Bayes(EB)检验问题.利用概率密度函数的核估计构造了参数的经验Bayes检验函数,并获得了它的渐近最优(a.o.)性,在适当的条件下证明了所提出的经验Bayes检验函数的收敛速度可任意接近O(n-1/2).     

Mixed Estimations and Bayes Estimation of theRegression Coefficient in Multivariate Linear Model

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On the accuracy of empirical likelihood confidence regions for linear regression model

The coverage errors of the empirical likelihood confidence regions for in a linear regression model,Y _i=x _i+ _i , 1in, are of ordern ^–1. Bartlett corrections may be employed to reduce the order of magnitude of the coverage errors ton ^–2. For practical implementation of Bartlett correction, an empirical Bartlett correction is given.     

New estimators of discriminant coefficients as the gradient of log-odds

We consider the problem of estimating the discriminant coefficients, η=∑^1-(θ⁽¹⁾-θ⁽²⁾) based on two independent normal samples fromN _p (θ⁽¹⁾,∑) andN _p (θ⁽²⁾,∑). We are concerned with the estimation of η as the gradient of log-odds between two extreme situations. A decision theoretic approach is taken with the quadratic loss function. We derive the unbiased estimator of the essential part of the risk which is applicable for general estimators. We propose two types of new estimators and prove their dominance over the traditional estimator using this unbiased estimator.     

Low order polynomial bounds on the expected performance of local improvement algorithms

We present a general abstract model of local improvement, applicable to such diverse cases as principal pivoting methods for the linear complementarity problem and hill climbing in artificial intelligence. The model accurately predicts the behavior of the algorithms, and allows for a variety of probabilistic assumptions that permit degeneracy. Simulation indicates an approximately linear average number of iterations under a variety of probability assumptions. We derive theoretical bounds of 2en logn and en ² for different distributions, respectively, as well as polynomial bounds for a broad class of probability distributions. We conclude with a discussion of the applications of the model to LCP and linear programming.The author was supported by the New Faculty Research Development Program of the Georgia Institute of Technology. This work is based on the author's Ph.D. thesis, performed under George Dantzig at Stanford 1978–81, at the Systems Optimization Laboratory. While at Stanford, research was supported in part by Department of Energy Contract AM03-76SF00326, PA #DE-AT03-76ER72018; Office of Naval Research Contract N00014-75-C-0267; National Science Foundation Grants MCS76-81259, MCS-7926009 and ECS-8012974; and Army Research Office Contract DAA29-79-C-0110. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.     

Semiparametric empirical likelihood estimation for two-stage outcome-dependent sampling under the frame of generalized linear models

Epidemiologic studies use outcome-dependent sampling （ODS） schemes where, in addition to a simple random sample, there are also a number of supplement samples that are collected based on outcome variable. ODS scheme is a cost-effective way to improve study efficiency. We develop a maximum semiparametric empirical likelihood estimation （MSELE） for data from a two-stage ODS scheme under the assumption that given covariate, the outcome follows a general linear model. The information of both validation samples and nonvalidation samples are used. What is more, we prove the asymptotic properties of the proposed MSELE.     

Empirical Bayes Test for the Parameter of Rayleigh Distribution with Error of Measurement

For the data with error of measurement in historical samples, the empirical Bayes test rule for the parameter of Rayleigh distribution is constructed, and the asymptotically optimal property is obtained. It is shown that the convergence rate of the proposed EB test rule can be arbitrarily close to O（n-1/2） under suitable conditions.     

The low of the iterated logarithm for empirical processes under absolute regularity

The compact law of the iterated logarithm for empirical processes whose underlying sequence satisfies a -mixing condition is considered. In particular, we show a compact law of the iterated logarithm for VC subgraph classes of functions, for classes of functions which satisfy the bracketing condition in Doukhanet al. ⁽⁶⁾ and for some classes of smooth functions.Research partially supported by NSF Grant DMS-93-02583.     

带有不完全信息随机截尾试验下最大似然估计的重对数律

本文在条件($\Phi$)下,证明了带有不完全信息随机截尾试验下最大似然估计的收敛速度符合重对数律,并验证了Weibull分布、对数正态分布满足条件($\Phi$).     

Bootstrapping the empirical distribution of a linear process

The validity of the moving block bootstrap for the empirical distribution of a short memory causal linear process is established under simple conditions that do not involve mixing or association. Sufficient conditions can be expressed in terms of the existence of moments of the innovations and summability of the coefficients of the linear model. Applications to one and two sample tests are discussed.     

Assessing the lifetime performance index of products with the exponential distribution under progressively type II right censored samples

In practice, lifetime performance index C_L is used to measure the potential and performance of a process, where L is the lower specification limit. Progressive censoring scheme is quite useful in many practical situations where budget constraints are in place or there is a demand for rapid testing. In this paper, under the assumption of exponential distribution, this study constructs a maximum likelihood estimator (MLE) of C_L based on the progressively type II right censored sample. The MLE of C_L is then utilized to develop the hypothesis testing procedure in the condition of known L. The new testing procedure can be employed by product managers to assess whether the lifetime of products (or items) adheres to the required level in the condition of known L. Finally, we give one example to illustrate the use of the testing algorithmic procedure under given significance level.     

The order of magnitude of the moments of the modulus of continuity of multiparameter poisson and empirical processes

In this note we derive the exact order of magnitude of the moments of the modulus of continuity for multiparameter Poisson and, almost as a corollary, for multivariate empirical processes.     

线性指数分布参数的经验Bayes检验问题

分别讨论了线性指数分布参数的经验Bayes(EB)单侧和双侧检验问题.利用概率密度函数的核估计分别构造了参数的经验Bayes检验函数,在适当的条件下证明了所提出的经验Bayes检验函数的渐近最优(a.o.)性并获得了它的收敛速度.最后,给出一个有关主要结果的例子.     

A tail empirical process approach to some nonstandard laws of the iterated logarithm

We show that a number of nonstandard laws of the iterated logarithm have limiting constants which may be expressed as the extreme values of functionals off, wheref varies over suitable compact sets of functions. By solving the corresponding extremal problems, we show how these constants are generated. In addition, several new laws are presented.