A Nonparametric Bootstrap Test for the Equality of Coefficients of Variation

The problem of testing the equality of coefficients of variation for two different populations leads to various levels of difficulty depending on the possible assumptions on models and parameters for the two populations under study. Simulation techniques appear to be the only feasible way in the case where the available information came only from data and when these do not allow one to make any assumption on the models. In this work we propose a nonparametric bootstrap procedure, both to build the test statistic and also to approximate the p-value. The properties of the test and its critical aspects are illustrated and discussed by means of an application to a real data set of anthropometric measures for the study of the sexual dimorphism.     

A NONPARAMETRIC TEST FOR THE EQUALITY OF DEPENDENT CORRELATION COEFFICIENTS UNDER NORMALITY

ABSTRACT

A nonparametric testing method for the equality of two correlation coefficients in trivariate normal distribution, namely, one of the variables are common, is discussed. Using a permutation test, we obtain asymptotically exact solutions. The performance of this test is compared with the likelihood ratio test and a method of using the limiting distribution of correlation coefficients.     

Bounds on Normal Approximations for the number of Descents and Inversions

In this article, we use Stein’s method to give non uniform bounds for normal approximation for the number of descents and inversions. Moreover, we also improve a constant on uniform bounds for normal approximation of those random variables in Fulman’s work in 2004. Our constants are 13.42 and 14.24, respectively.     

Step-Down Multiple Comparison Procedures Using Medians and Permutation Tests

Richter and McCann (2007 Richter , S. J. , McCann , M. H. ( 2007 ). Multiple comparisons using medians and permutation tests . Journal of Modern Applied Statistical Methods 6 ( 2 ): 399 – 412 . [Google Scholar]) presented a median-based multiple comparison procedure for assessing evidence of group location differences. The sampling distribution was based on the permutation distribution of the maximum median difference among all pairs, and provides strong control of the FWE. This idea is extended to develop a step-down procedure for comparing group locations. The new step-down procedure exploits logical dependencies between pairwise hypotheses and provides greater power than the single-step procedure, while still maintaining strong FWE control. The new procedure can also be a more powerful alternative to existing methods based on means, especially for heavy-tailed distributions.     

Comparing Two Survival Time Distributions: An Investigation of Several Weight Functions for the Weighted Logrank Statistic

In survival analysis, it is often of interest to test whether or not two survival time distributions are equal, specifically in the presence of censored data. One very popular test statistic utilized in this testing procedure is the weighted logrank statistic. Much attention has been focused on finding flexible weight functions to use within the weighted logrank statistic, and we propose yet another. We demonstrate our weight function to be more stable than one of the most popular, which is given by Fleming and Harrington, by means of asymptotic normal tests, bootstrap tests and permutation tests performed on two datasets with a variety of characteristics.     

The Performance of Randomization Tests that Use Permutations of Independent Variables

ABSTRACT

In this article we evaluate the performance of a randomization test for a subset of regression coefficients in a linear model. This randomization test is based on random permutations of the independent variables. It is shown that the method maintains its level of significance, except for extreme situations, and has power that approximates the power of another randomization test, which is based on the permutation of residuals from the reduced model. We also show, via an example, that the method of permuting independent variables is more valuable than other randomization methods because it can be used in connection with the downweighting of outliers.     

A Class of Permutation Tests for the Equality of Two Marginal Survival Functions Using Paired Censored Data

We studied several test statistics for testing the equality of marginal survival functions of paired censored data. The null distribution of the test statistics was approximated by permutation. These tests do not require explicit modeling or estimation of the within-pair correlation, accommodate both paired data and singletons, and the computation is straightforward with most statistical software. Numerical studies showed that these tests have competitive size and power performance. One test statistic has higher power than previously published test statistics when the two survival functions under comparison cross. We illustrate use of these tests in a propensity score matched dataset.     

Preliminary Goodness-of-Fit Tests for Normality do not Validate the One-Sample Student t

One of the most basic topics in many introductory statistical methods texts is inference for a population mean, μ. The primary tool for confidence intervals and tests is the Student t sampling distribution. Although the derivation requires independent identically distributed normal random variables with constant variance, σ², most authors reassure the readers about some robustness to the normality and constant variance assumptions. Some point out that if one is concerned about assumptions, one may statistically test these prior to reliance on the Student t. Most software packages provide optional test results for both (a) the Gaussian assumption and (b) homogeneity of variance. Many textbooks advise only informal graphical assessments, such as certain scatterplots for independence, others for constant variance, and normal quantile–quantile plots for the adequacy of the Gaussian model. We concur with this recommendation. As convincing evidence against formal tests of (a), such as the Shapiro–Wilk, we offer a simulation study of the tails of the resulting conditional sampling distributions of the Studentized mean. We analyze the results of systematically screening all samples from normal, uniform, exponential, and Cauchy populations. This pretest does not correct the erroneous significance levels and makes matters worse for the exponential. In practice, we conclude that graphical diagnostics are better than a formal pretest. Furthermore, rank or permutation methods are recommended for exact validity in the symmetric case.     

A Decomposition of Copulas and Its Use

ABSTRACT

In this article, we create a decomposition that represents and describes the depen-dence structure between two variables. Since copulas provide a deep understanding of the dependence structure by eliminating the effects of the marginals, they play a key role in this study. We define a discretized copula density matrix and decompose it into a set of permutation matrices by using the Birkhoff–von Neumann theorem. This decomposition provides a way to effectively apply the concepts of copulas to solve problems in multivariate statistical data analysis.     

Permutation Matrix with Application to Optimal Invariant Quadratic Prediction in Finite Populations

In this article, we primarily aim to apply the permutation matrix techniques to the problem of the optimal invariant quadratic prediction in a finite population. An alternative to the work of Liu and Rong (2007 Liu , X. , Rong , J. ( 2007 ). Quadratic prediction problems in finite populations . Statist. Probab. Lett. 77 : 483 – 489 .[Crossref], [Web of Science ®] , [Google Scholar]) is offered. In addition, we derive the OIQP for the population variance and show that it has less PMSE than the ordinary optimal unbiased predictor.