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Tests of Hypotheses for Model Parameters

  • Victor M. Panaretos
Chapter
  • 3.6k Downloads
Part of the Compact Textbooks in Mathematics book series (CTM)

Abstract

This chapter considers the problem of hypothesis testing. Starting from first principles, it develops the Neyman-Pearson framework, and discusses different forms of hypothesis pairs. It then uses the question of optimality of tests as a means for motivating specific test functions. This is done in a general setup for simple-vs-simple hypotheses, and in an exponential family context for one-sided alternatives. The likelihood ratio method and Wald’s method are then introduced, to address the more general case of two-sided alternatives. Asymptotic approximations are then used in order to determine approximate critical values in the context of exponential families. The chapter concludes with the introduction of p-values, their basic properties, and their relation to the Neyman-Pearson paradigm.

Keywords

Likelihood Ratio Test Exponential Family Optimal Test Bernoulli Variable Likelihood Ratio Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Victor M. Panaretos
    • 1
  1. 1.Institute of MathematicsEPFLLausanneSwitzerland

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