Normality Of Linear Rank Statistics Research Articles

On asymptotic normality of certain linear rank statistics

We consider asymptotic normality of linear rank statistics under various randomization rules met in clinical trials. Exposition relies on some general limit theorem given in McLeish (1974). Examples of applications include well known results as well as new ones. Though exposition is tightly attached to the context of clinical trials, the obtained results equally well apply to situations where randomization of similar kind takes place.

Lp nonuniform bounds for asymptotic normality of linear rank statistics

An L p , 1 ⩽ p ⩽ ∞, nonuniform central limit order bound O(N − 1 2 ) for simple linear rank statistics is obtained. The theorem is proved for a wide class of scores including the van der Waerden scores and the Wilcoxon scores. It extends and improves some known results obtained in this direction.

Asymptotic normality and convergence rates of linear rank statistics under alternatives

Abstract : Asymptotic normality of linear rank statistics under alternatives is proved employing techniques of Chernoff and Savage. Under suitable assumptions the rate of convergence to normality under alternatives is also obtained for such statistics. The results of the paper are related to those of Hajek and Hoeffding. Results on the rate of convergence extend those of Jureckova and Puri and Bergstrom and Puri.

On the asymptotic normality of linear rank statistics

A method for proving the asymptotic normality of linear rank statistics is presented. Use is made of the fact that the variances of many rank statistics met in practice admit a factorization expressed in terms of the sample size. The method of proof consists of two steps corresponding to the limiting behavior of the modulus and argument of the characteristic function of the rank statistic.

Asymptotic Normality of Nonparametric Tests for Independence

Asymptotic normality of linear rank statistics for testing the hypothesis of independence is established both under fixed alternatives (or the null hypothesis) and under converging alternatives. The results of Ruymgaart, Shorack and van Zwet [14] are used to obtain a further weakening of the smoothness conditions on the score functions. In the present case the score functions are allowed to have a finite number of discontinuities of the first kind. The results of the present paper and of the paper [14] will be summarized in the author's thesis [13].

ON TESTS OF SYMMETRY FOR DISCRETE POPULATIONS

SummaryIn this paper problems of tests of symmetry about the origin with discrete samples are considered. Recently Vorličková established the asymptotic normality of linear rank statistics and signed rank statistics in [5] and [6]. Here we propose statistics which are conditionally the sum of independent variables, including the locally most powerful tests for a one sided one parameter family. Their asymptotic distributions are derived under the null hypothesis and the contiguous rounding off location alternatives. We propose four types of signed rank tests and investigate their properties.

Asymptotic Normality of Nonparametric Tests for Independence

Asymptotic normality of linear rank statistics for testing the hypothesis of independence is established under fixed alternatives. A generalization of a result of Bhuchongkul [1] is obtained both with respect to the conditions concerning the orders of magnitude of the score functions and with respect to the smoothness conditions on these functions.

Linear Functions of Order Statistics

Linear Functions of Order Statistics