Confidence Intervals and Tests for Variance Ratios in Unbalanced Variance Components Models

Confidence intervals for variance components and functions of variance components in the random effects model under non-normality

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii CHAPTER 1. GENERAL INTRODUCTION . . . . . . . . . . . . . . . . . . . 1 1.1 One-way Random Effects ANOVA Model . . . . . . . . . . . . . . . . . . . . . 1 CHAPTER 2. REVIEW OF LITERATURE . . . . . . . . . . . . . . . . . . . . 5 2.1 The Statistical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

U-tests for variance components in linear mixed models

We propose U -statistics-based tests for null variance components in linear mixed models. We obtain their asymptotic distribution (for increasing number of units) under mild regularity conditions that include only the existence of the second moment for the distribution of the random effects and of the fourth moment for the distribution of the conditional errors. We also derive their nonnull dis...

Tests for Variance Components in Varying Coefficient Mixed Models

We consider a general class of varying coefficient mixed models where random effects are introduced to account for between-subject variation. To address the question of whether a varying coefficient mixed model can be reduced to a simpler varying coefficient model, we develop one-sided tests for the null hypothesis that all the variance components are zero. In addition to the purely null-based ...

Honest Confidence Intervals for the Error Variance in Stepwise Regression

An honest confidence interval for the error variance in a stepwise regression is a one-sided interval that adjusts for the effects of variable selection. The endpoint of this interval may be many times larger than the usual endpoint. Such adjustments are most important when selecting variables from a large number of available predictors, particularly in situations with more available predictors...

Variance Estimation and Construction of Confidence Intervals for GEE Estimator