Confidence intervals for variance components and functions of variance components in the random effects model under non-normality
نویسندگان
چکیده
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.1 Wald Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2.2 Exact Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2.3 Approximate Normal Theory Confidence Intervals . . . . . . . . . . . . 8 2.3 Effects of Non-normality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3.1 Monte Carlo Simulation Study Results . . . . . . . . . . . . . . . . . . . 9 2.3.2 Detecting Kurtosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 CHAPTER 3. METHODS FOR σ2 α . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.1 Proposed Method for σ2 α . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2 Monte Carlo Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2.1 Errors Distributed Normal . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.2.2 Errors Distributed Non-Normal . . . . . . . . . . . . . . . . . . . . . . . 20 3.2.3 Varying the value of σ2 α . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3 Methods Using Prior Kurtosis Information . . . . . . . . . . . . . . . . . . . . . 21 3.3.1 Kurtosis Estimates from Previous Studies . . . . . . . . . . . . . . . . . 21
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