An example of a two-sided Wilcoxon signed rank test which is not unbiased

Although the theory of rank tests is rather complete in the one-sided case, it was not even known in 1959, whether the Wilcoxon two-sample test and other similar tests are unbiased against the two-sided alternatives (Lehmann (1959,Testing Statistical Hypotheses, p. 240, Wiley, New York)). A partial answer to this question was given by Sugiura in 1965, who found, that the test named above may be biased (Sugiura (1965,Ann. Inst. Statist. Math.,17, 261–263)). According to Lehmann (1986,Testing Statistical Hypotheses, 2nd ed., pp. 322–324, Wiley, New York) it seems to be still open, whether the same is true for the WILCOXON one-sample test, which is also known as WILCOXON signed rank test. This will be shown in the present paper.     

Unbiased Bayes estimates and improper priors

Given two random variables (X, Y) the condition of unbiasedness states that:E(X |Y=y)=y andE(Y |X=x)=x both almost surely (a.s.). If the prior onY is proper and has finite expectation or non-negative support, unbiasedness impliesX=Y a.s. This paper examines the implications of unbiasedness when the prior onY is improper. Since the improper case can be meaningfully analysed in a finitely additive framework, we revisit the whole issue of unbiasedness from this perspective. First we argue that a notion weaker than equality a.s., named coincidence, is more appropriate in a finitely additive setting. Next we discuss the meaning of unbiasedness from a Bayesian and fiducial perspective. We then show that unbiasedness and finite expectation ofY imply coincidence betweenX andY, while a weaker conclusion follows if the improper prior onY is only assumed to have positive support. We illustrate our approach throughout the paper by revisiting some examples discussed in the recent literature.This work was partially supported by C.N.R. grant N.80.02970.10 (G.C.) and by C.N.R. grant altri interventi (P.V.). A preliminary draft was written while the Authors were visiting the Department of Statistics at Carnegie Mellon University.The paper is the result of close cooperation between the two authors. However subsections 3.1 and 3.3 are mainly due to G.C. while subsection 3.2 and section 4 are mainly due to P.V.     

On some multivariate density estimates and empirical Bayes problems

This paper consider estimates of multidimensional density functions and their derivatives. The asymptotic unbiasedness and the convergence properties of these estimates are established.Some applications to empirical Bayes problems are considered.     

门限自回归模型的非参数估计

对一维一阶一个门限的ＴＡＲ模型，通过模型所构成的Ｍａｒｋｏｖ链的遍历性，得到了其核密度估计的渐近无偏性，均方相容性和渐近正态性     

Maximum variance unimodal distributions

A new sufficient condition for the variance of a unimodal distribution in ?a, b? to have the least upper bound $\text{(b ? a)}{}^2\text{12}$ is derived. This condition is more general than the condition found by Jacobson (1969). A new proof that the least upper bound for all unimodal distributions in ?a, b? is $\text{(b ? a)}{}^2\text{9}$ is also given. These results are used to construct a new estimator of the variance of such distributions.     

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.     

Robust regression credibility: The influence function approach

In classical credibility theory we assume that the vector of claims conditionally on has independent components with identical means. However, this assumption is sometimes unrealistic. To relax this condition Hachemeister (Hachemeister, C.A., 1975. Credibility for regression models with application to trend. In: Kahn, P. (Ed.), Credibility, Theory and Applications. Academic Press, New York) introduced regressors. The presence of large claims can perturb the credibility premium estimation. The lack of robustness of regression credibility estimators, as well as the fairness of tariff evaluation, led to the development of this paper. Our proposal is to apply robust statistics to the regression credibility estimation by using the robust influence function approach of M-estimators.     

Two-Stage Likelihood Ratio and Union–Intersection Tests for One-Sided Alternatives Multivariate Mean with Nuisance Dispersion Matrix

For a multinormal distribution with an unknown dispersion matrix, union-intersection (UI) tests for the mean against one-sided alternatives are considered. The null distribution of the UI test statistic is derived and its power monotonicity properties are studied. A Stain-type two-stage procedure is proposed to eliminate some of the inherent drawbacks of such tests. Some comparisons are also made with some recently proposed alternative conditional likelihood ratio tests.     

δ修正Cramr-von Mises检验的非无偏性(英文)

在简单假设下,证明了对任意给定水平α∈(0,1)和样本容量n,δ修正Cramr-von Mises检验的非无偏性.     

MOBVE分布参数的估计及其改进

本文讨论由Marshall和Olkin引进的二元指数分布(MOBVE分布)的参数估计问题.这个分布关于某个控制测度的密度函数被提出.对于边缘分布相同的情形,本文给出了充分统计量并讨论了它的性质;对两个参数各提出了一个无偏估计并采用协方差改进法分别对其作了改进.