Likelihood Ratio Tests for Principal Components

Likelihood Ratio Tests for

Likelihood Ratio Tests in Multivariate Variance Components Models

ii Acknowledgements In preparing this thesis I am indebted to many people. First of all, I wish to express my sincere gratitude to Professor Chihiro Hirotsu, my thesis supervisor, for his guidance and encouragement. Komaki for their valuable comments and suggestions. Finally I am very grateful to my parents for their continual encouragement, and to my wife, Hisae, who has shared both my joy and...

On likelihood ratio tests

Likelihood ratio tests are intuitively appealing. Nevertheless, a number of examples are known in which they perform very poorly. The present paper discusses a large class of situations in which this is the case, and analyzes just how intuition misleads us; it also presents an alternative approach which in these situations is optimal. 1. The popularity of likelihood ratio tests Faced with a new...

Likelihood Ratio Tests

Many statistical hypotheses can be formulated in terms of polynomial equalities and inequalities in the unknown parameters and thus correspond to semi-algebraic subsets of the parameter space. We consider large sample asymptotics for the likelihood ratio test of such hypotheses in models that satisfy standard probabilistic regularity conditions. We show that the assumptions of Chernoff's theore...

Likelihood Ratio Tests

Previously, we have employed a program (Jtest) to test an hypothesis involving many parameters (multiple constraints). This test, which involves comparing parameter estimates with hypothesized values, is known as a Wald test. We also used the Jtest program to compare two di¤erent estimators in a Hausman test. There is an alternative method for conducting joint tests, which can be implemented ea...