The 3/2th and 2nd order asymptotic efficiency of maximum probability estimators in non-regular cases

In this paper we consider the estimation problem on independent and identically distributed observations from a location parameter family generated by a density which is positive and symmetric on a finite interval, with a jump and a nonnegative right differential coefficient at the left endpoit. It is shown that the maximum probability estimator (MPE) is 3/2th order two-sided asymptotically efficient at a point in the sense that it has the most concentration probability around the true parameter at the point in the class of 3/2th order asymptotically median unbiased (AMU) estimators only when the right differential coefficient vanishes at the left endpoint. The second order upper bound for the concentration probability of second order AMU estimators is also given. Further, it is shown that the MPE is second order two-sided asymptotically efficient at a point in the above case only.Research supported by University of Tsukuba Project Research.     

Second order asymptotic optimality of estimators for a density with finite cusps

We consider i.i.d. samples from a continuous density with finite cusps. Then we obtain the bound for the second order asymptotic distribution of all asymptotically median unbiased estimators. Further we get the second order asymptotic distribution of a bias-adjusted maximum likelihood estimator, and we see that it is not generally second order asymptotically efficient.     

一维双边截断型分布族中参数函数的经验Bayes估计及其收敛速度

对一维双边截断型分布族构造了参数函数的经验 Ｂａｙｅｓ 估计,在适当的条件下给出了相应的收敛速度,并说明此收敛速度可充分接近 １２ ．     

Asymptotic efficiency of the Spearman estimator and characterizations of distributions

Summary The Spearman estimator is designed to be a nonparametric estimator for the expectation of a tolerance distribution. We characterize the one-parameter families of distributions (the parameter being the mean of the distribution) for which the Spearman estimator has asymptotic efficiency one. In particular, when the parameter indexes the location, the characterizing distribution is the logistic distribution. In any other case of efficiency one, the family of distributions is given by certain transformations of a logistic distribution. The author's research is supported by a Grant from the Office of Naval Research, Grant No. N00014-84-K-0184. Reproduction in whole or in part is permitted for any purpose of the U.S. Government. The author's research is supported by the Royal Norwegian Council for Scientific and Industrial Research.     

左截断右删失下核密度估计的L1距离的界

本文在左截断右删失数据下获得了概论密度的核估计的L1距离的一个上界．     

Local asymptotic normality and asymptotical minimax efficiency of the MLE under random censorship

Here we study the problems of local asymptotic normality of the parametric family of distributions and asymptotic minimax efficient estimators when the observations are subject to right censoring. 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 furthermore 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.     

Third order efficiency implies fourth order efficiency: A resolution of the conjecture of J. K. Ghosh

Under suitable regularity conditions, it is shown that a third order asymptotically efficient estimator is fourth order asymptotically efficient in some class of estimators in the sense that the estimator has the most concentration probability in any symmetric interval around the true parameter up to the fourth order in the class. This is a resolution of the conjecture by Ghosh (1994, Higher Order Asymptotics, Institute of Mathematical Statistics, Hayward, California). It is also shown that the bias-adjusted maximum likelihood estimator is fourth order asymptotically efficient in the class.     

绝对损失下双边截断型分布族参数的渐近最优经验Bayes估计

本文在绝对损失下构造了双边截断型分布族参数的经验Bayes估计,并在合适的条件下证明了该估计的渐近最优性.最后,给出两个有关本文主要结果的例子.     

删失截断情形下失效率变点模型的Bayes参数估计

通过添加部分缺失寿命变量数据,得到了删失截断情形下失效率变点模型相对简单的似然函数.讨论了所添加缺失数据变量的概率分布和随机抽样方法.利用Monte Carlo EM算法对未知参数进行了迭代.结合Metropolis-Hastings算法对参数的满条件分布进行了Gibbs抽样,基于Gibbs样本对参数进行估计,详细介绍了MCMC方法的实施步骤.随机模拟试验的结果表明各参数Bayes估计的精度较高.     

Minimax and admissible minimax estimators of the mean of a multivariate normal distribution for unknown covariance matrix

Let X be a p-variate (p ≥ 3) vector normally distributed with mean μ and covariance Σ, and let A be a p × p random matrix distributed independent of X, according to the Wishart distribution W(n, Σ). For estimating μ, we consider estimators of the form δ = δ(X, A). We obtain families of Bayes, minimax and admissible minimax estimators with respect to the quadratic loss function (δ ? μ)′ Σ^?1(δ ? μ) where Σ is unknown. This paper extends previous results of the author [1], given for the case in which the covariance matrix of the distribution is of the form σ²I, where σ is known.     

关于可靠性生存寿命分析中几类重要截尾分布函数参数的最佳有效无偏估计

在给出了可靠性生存寿命分析几类重要随机截尾分布函数的基础上,讨论了寿命分布函数参数的最佳有效无偏估计,为解决可靠性生存寿命分析以及通讯工程和电力负载预测中的最佳无偏误差估计问题提供了令人满意的可靠依据和有效算法．