ROBUSTNESS OF TRIMMED F STATISTIC WHEN HANDLING NONNORMAL DATA

The Trimmed Lasso: Sparsity and Robustness

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control over the desired level of sparsity of estimators. We analyze its structural properties and in doing so show the following: 1. Drawing parallels between robus...

Evaluating the robustness of repeated measures analyses: the case of small sample sizes and nonnormal data.

Repeated measures analyses of variance are the method of choice in many studies from experimental psychology and the neurosciences. Data from these fields are often characterized by small sample sizes, high numbers of factor levels of the within-subjects factor(s), and nonnormally distributed response variables such as response times. For a design with a single within-subjects factor, we invest...

A Comparison of the Power of Wilcoxon's Rank-Sum Statistic to That of Student's t Statistic under Various Nonnormal Distributions

Computer generated Monte Carlo techniques were used to compare the power of Wilcoxon's rank-sum test to the power of the two independent means t test for situations in which samples were drawn from (1) uniform, (2) Laplace, (3) halfnormal, (4) exponential, (5) mixed-normal, and (6) mixeduniform distributions. Sample sizes studied were (n ,n) = (3,9), (6,6), (9,27), (18,18), (27,81), and (54,54)...

Power Analyses When Comparing Trimmed Means

Robustness and accuracy of methods for high dimensional data analysis based on Student’s t statistic

Student’s t statistic is finding applications today that were never envisaged when it was introduced more than a century ago. Many of these applications rely on properties, for example robustness against heavy tailed sampling distributions, that were not explicitly considered until relatively recently. In this paper we explore these features of the t statistic in the context of its application ...