On asymptotically Risk-effivient sequential versions of generalized U-statistics

Sequential point estimation of means of generalized U-statistics is considered. Based on a well defined stopping rule, the proposed sequential (estimation) procedure is shown to be asymptotically (first order) risk-efficient. Asymptotic distributions of sequential generalized U-statistics and the allied stopping times are also studied.     

一类U统计量函数的Edgeworth展开

利用函数的泰勒展开,考虑了一类U统计量函数的Edgeworth展开问题.分别在函数的三、四阶导数有界等条件的假设下,给出了一类U统计量函数的Edgeworth展开式.     

随机加数U-统计量

本文基于刀切虚拟值提出了对U-统计量的随机加权法。证明了一些渐近性质并讨论了Bootstrap与随机加权法之间的关系。     

A Note on Shortest Prediction Intervals for Log-Linear Regression

Analytical and Monte Carlo results are used to investigate the robustness of the exact statistical test suggested by Nelson for testing the hypothesis of equality of two availabilities. A non-parametric test based on a generalized U-statistic is proposed which does not depend on the assumption that the times to failure and times to repair are exponentially distributed. Additional Monte Carlo results are used to point out the strengths and weaknesses of this test.     

广义U统计量的随机加权法

本文对广义u—统计量的未知分布建立了随机加权逼近,证明了逼近的相合性定理。     

Some comments on specification tests in nonparametric absolutely regular processes

In this note, several aspects of a recently proposed specification test in nonparametric models driven by an absolutely regular process are discussed. In particular, we give a more detailed asymptotic analysis of tests based on kernel methods under fixed alternatives using a central limit theorem for U-statistics with n-dependent nondegenerate kernel. As a by-product, it is demonstrated that several results regarding the asymptotic distribution or goodness-of-fit tests are incorrectly stated in the literature. Our result also indicates that results on the asymptotic equivalence of nonparametric autoregression and nonparametric regression cannot be used for the asymptotic analysis of goodness-of-fit tests under fixed alternatives.     

On the subsample bootstrap variance estimation

In this paper we further elaborate on the subsample bootstrap result of Politis and Romano. Combining the jackknife and bootstrap ideas we were able to establish a wide consistency for the subsample bootstrap variance estimator. This was confirmed by simulations. Research partly supported by NSF Grant No. DMS-93-00725     

A New Class of Distribution-Free Tests for Location Parameters

Abstract

A new class of distribution-free tests for the two-sample location problem is proposed. The tests are based on two-sample U-statistics. This class basically generalizes the tests proposed by Deshpande, J.V.; Kochar, S.C. Some competitors of Wilcoxon–Mann–Whitney test for location alternatives. Journal of Indian Statistical Association 1982, 19, 9–18. The proposed class of tests is also extended to the k (≥ 2)-sample problem for testing homogeneity of location parameters against ordered alternatives. This extension is based on linear combinations of two-sample U-statistics. Pitman asymptotic relative efficiencies (AREs) of the members of the proposed class(es) of tests relative to some of the existing tests are computed for a number of underlying distributions. It is shown that the proposed class of tests performs as good as or better than its competitors in literature.