Supersmooth testing on the sphere over analytic classes

We consider the nonparametric goodness-of-fit test of the uniform density on the sphere when we have observations whose density is the convolution of an error density and the true underlying density. We will deal specifically with the supersmooth error case which includes the Gaussian distribution. Similar to deconvolution density estimation, the smoother the error density the harder is the rate recovery of the test problem. When considering nonparametric alternatives expressed over analytic classes, we show that it is possible to obtain original separation rates much faster than any logarithmic power of the sample size according to the ratio of the regularity index of the analytic class and the smoothness degree of the error. Furthermore, we show that our fully data-driven statistical procedure attains these optimal rates.     

ON TESTING AGAINST RESTRICTED ALTERNATIVES FOR THE VARIANCES OF GAUSSIAN MODELS

Let π₁,…,π_p be p independent normal populations with means μ₁…, μ_p and variances σ²₁,…, σ²_p respectively. Let X(n_i) be a simple random sample of size n_i from π_i, i = 1,…,p. Given the simple random samples X(n₁),…, X(n_p) from π₁,…,π_p respectively, a test has been proposed for testing the homogeneity of variances H₀: σ²₁=…σ²_p, against the restricted alternative, H₁: σ²₁≥…≥σ²_p, with at least one strict inequality. Some properties of the test are discussed and critical values are tabulated.     

Bayes two-decision procedures for two-sample problems and rank-order data

A two-sample problem for rank-order data is formulated as a two-decision problem. Using the general Bayes solution, Bayes procedures are derived for several configurations of the set of states of nature including some for which the problem is distribution-free. It is shown that for certain prior distributions these procedures reduce to classical LMP rank tests. Some devices for selection of prior distributions are suggested. It is shown that the Bayes risk of these procedures tends to zero as sample sizes increase.     

WILCOXON-TYPE RANK-SUM PRECEDENCE TESTS

This paper introduces Wilcoxon‐type rank‐sum precedence tests for testing the hypothesis that two life‐time distribution functions are equal. They extend the precedence life‐test first proposed by Nelson in 1963. The paper proposes three Wilcoxon‐type rank‐sum precedence test statistics—the minimal, maximal and expected rank‐sum statistics—and derives their null distributions. Critical values are presented for some combinations of sample sizes, and the exact power function is derived under the Lehmann alternative. The paper examines the power properties of the Wilcoxon‐type rank‐sum precedence tests under a location‐shift alternative through Monte Carlo simulations, and it compares the power of the precedence test, the maximal precedence test and Wilcoxon rank‐sum test (based on complete samples). Two examples are presented for illustration.     

A modified chi-square test of independence against a class of ordered alternatives in an r x c contingency table

A modified chi-square test statistic is constructed for testing the hypothesis of independence in a two-way contingency table against a class of ordered alternatives defined in terms of pooled cross-product ratios. The test procedure can also be used to test for positive quadrant dependence in a two-way contingency table. The asymptotic distribution of the test statistic under the null hypothesis is obtained. Some power comparisons with known test procedures are given. A numerical example is given to illustrate the use of this test.     

On Local Power Properties of Frequency Domain‐based Tests for Stationarity

A framework for the asymptotic analysis of local power properties of tests of stationarity in time series analysis is developed. Appropriate sequences of locally stationary processes are defined that converge at a controlled rate to a limiting stationary process as the length of the time series increases. Different interesting classes of local alternatives to the null hypothesis of stationarity are then considered, and the local power properties of some recently proposed, frequency domain‐based tests for stationarity are investigated. Some simulations illustrate our theoretical findings.     

Testing homoosenetty of t normal means against ordered alternatives in 2 groups having uncommon and unknown variance

Given two series of normal populations with variances unknown and common within the series but possibly differ between the series, the likelihood ratio test of simultaneous homogeneity of means against sinpie order alternative is considered. Sole approxirations Par the null distribution of thetest statistic are also proposed.     

Distribution of ranks in a two-sample problem with right censored data

We consider different censoring models for a two-sample and find the joint distribution of the rank vector and number of uncensored observations under each censoring model when the distributions of life times and/or distributions of censoring of censoring variables satisfy the condition for the Lehmann type of alternatives.     

On shrinkage r-estimation in a multiple regression model

For a multiple regression model, bearing the plausibility of a subset of the regression parameters being close to a pivot, for the complementary subset, based on the usual James-Stein rule, a general formulation of shrinkage R-estimation is considered. In the light of asymptotic distributional risks of estimators, performance characteristics ( under local alternatives) of the classical R-est-imator and its preliminary test and shrinkage versions (all based on the common score function ) are studied. These shed light on the relative dominance picture in a meaningful asymptotic setup.     

Shrinkage estimation in replicated median ranked set sampling

In this article, we consider the median ranked set sampling estimation and test of hypothesis for the mean for symmetric distributions. We suggest some alternative estimation strategies for parameters based on shrinkage and pretest principles. It is advantageous to use the non-sample information in the estimation process to construct alternative estimations for the parameter of interest. In this article, large sample properties of the suggested estimators will be assessed numerically using computer simulation. The relative performance of the suggested estimators for moderate and large samples will also be simulated. For illustration purposes, the proposed methodology is applied using data collocated from the Pepsi Cola production company in Al-Khobar, Saudi Arabia.