日期精度：到日 21 篇 · 到月 14 篇 · 到年 2 篇
单样本秩统计量的不变性原理
Analogous to the Donsker theorem on partial cumulative sums of independent random variables, for a broad class of one-sample rank order statistics, weak convergence to Brownian motion processes is studied here. A simple proof of the asymptotic normality of these statistics for random sample sizes is also presented. Some asymptotic results on renewal theory for one-sample rank order statistics are derived.
For one sample rank order statistics, a law of iterated logarithm and almost sure convergence to Wiener processes are established here. For the one-sample location problem, a sequential test procedure based on rank order statistics is proposed, and with the aid of the earlier results, it is shown that this has power one and arbitrarily small type I error.
纤维束强度的固定宽度置信带
The present paper deals with the asymptotic theory of sequential confidence intervals of prescribed width $2d (d > 0)$ and prescribed coverage probability $1 - \alpha (0 < \alpha < 1)$ for the (unknown, per unit) strength of bundle of parallel filaments. In this context, certain useful convergence results on the empirical distribution and on the bundle strength of filaments are established and incorporated in the proofs of the main theorems. The results are the sequential…
纵向研究中的非参数方法
Inference procedures based on some simple rank statistics are proposed and studied for the statistical analysis of longitudinal data. These robust and asymptotically efficient procedures do not require the basic assumption of multivariate normality of the underlying distributions. The theory is illustrated with two examples.
基于 Kendall 秩相关系数的回归系数估计
The least squares estimator of a regression coefficient β is vulnerable to gross errors and the associated confidence interval is, in addition, sensitive to non-normality of the parent distribution. In this paper, a simple and robust (point as well as interval) estimator of β based on Kendall's [6] rank correlation tau is studied. The point estimator is the median of the set of slopes (Yj - Yi )/(tj-ti ) joining pairs of points with ti ≠ ti , and is unbiased. The confidence…
若干多元位置问题的非参数置信域
Nonparametric methods of constructing confidence regions for the location vectors in the multivariate one-sample and two-sample problems are provided. These methods are based on a class of rank order statistics studied in detail by the authors in [8, 9, 11, 13]. Specifically, nonparametric confidence regions based on the Bonferroni inequality, the maximum modulus, and Scheffé's method are studied. The results obtained are nonparametric generalizations of some of the results…
若干多元位置问题的非参数置信区域
Nonparametric methods of constructing confidence regions for the location vectors in the multivariate one-sample and two-sample problems are provided. These methods are based on a class of rank order statistics studied in detail by the authors in [8, 9, 11, 13]. Specifically, nonparametric confidence regions based on the Bonferroni inequality, the maximum modulus, and Scheffé's method are studied. The results obtained are nonparametric generalizations of some of the results…
基于 n 排序法的渐近有效检验
Summary The problem of finding asymptotically most powerful analysis of variance tests by the method of n rankings is studied here. In this context, characterizations of the optimality of the well-known tests by Friedman (1937) and Brown and Mood (1951) are also considered.
双向布局中的若干最优非参数程序
Some optimum nonparametric procedures for estimating and testing contrasts in two-way layouts are proposed and studied. These procedures are based on the Chernoff-Savage [4] type of rank order statistics which include the Wilcoxon and normal scores statistics among others. In the first three sections, the properties of the proposed point estimators of contrasts, such as symmetry, invariance and asymptotic normality, are studied and their asymptotic relative efficiencies with…
关于 Friedman 检验渐近效率的札记
The robustnese-efficiency of Friodman's (1937) xr2-test for heteroscedastic error components is established here. Further, when the error components are homoscedastic but not identically distributed, some bounds for the asymptotic efficiency of xr2-test are derived.
m 依赖时间序列的若干非参数检验
In the case of moving average schemes or what are termed the m-dependent stochastic processes, the successive observations in the series are not stochastically independent. As a result, the usual sign test, the test based on the rank correlation τ (for randomness against trend alternatives), and the test proposed by Moore and Wallis [9] and further developed by Goodman and Grunfeld [2] (for the comovement between two time series) are not valid and require some modifications.…