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Statistical Theory and Inference

  • David J. Olive

Table of contents

  1. Front Matter
    Pages i-xii
  2. David J. Olive
    Pages 1-27
  3. David J. Olive
    Pages 81-99
  4. David J. Olive
    Pages 101-128
  5. David J. Olive
    Pages 129-155
  6. David J. Olive
    Pages 157-182
  7. David J. Olive
    Pages 183-213
  8. David J. Olive
    Pages 215-256
  9. David J. Olive
    Pages 257-290
  10. David J. Olive
    Pages 291-357
  11. David J. Olive
    Pages 359-371
  12. David J. Olive
    Pages 373-413
  13. Back Matter
    Pages 415-434

About this book

Introduction

This text is for  a one semester graduate course in statistical theory and covers minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, bias and mean square error, uniform minimum variance estimators and the Cramer-Rao lower bound, an introduction to large sample theory, likelihood ratio tests and uniformly most powerful  tests and the Neyman Pearson Lemma. A major goal of this text is to make these topics much more accessible to students by using the theory of exponential families.

Exponential families, indicator functions and the support of the distribution are used throughout the text to simplify the theory. More than 50 ``brand name" distributions are used to illustrate the theory with many examples of exponential families, maximum likelihood estimators and uniformly minimum variance unbiased estimators. There are many homework problems with over 30 pages of solutions.

Keywords

exponential familes large sample theory point estimators statistical inference statistical theory

Authors and affiliations

  • David J. Olive
    • 1
  1. 1.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

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