• 1 INTRODUCTION
  • 2 THE NEYMAN-PEARSON PARADIGM
  • 3 CONTROL OF THE SIZE OF A TEST
  • 3.1 p-Values
  • 3.2 The Bahadur-Savage Result
  • 4 OPTIMALITY CONSIDERATIONS
  • 4.1 UMPU Tests
  • 4.2 Conditional Tests
  • 4.3 UMPI Tests
  • 4.4 Monotone Tests
  • 4.5 Maximin Tests
  • 4.6 Tests Maximizing Average or Weighted Power
  • 4.7 Locally Most Powerful Tests
  • 5 LARGE-SAMPLE CONSIDERATIONS
  • 5.1 Asymptotic Optimality
  • 6 METHODS FOR HYPOTHESIS TESTING
  • 6.1 Testing in Parametric Models using Likelihood Methods
  • 6.2 Testing in the Extremum Estimation Framework
  • 7 CONSTRUCTION OF CRITICAL VALUES
  • 7.1 Randomization Methods
  • 7.2 Bootstrap
  • 7.3 Subsampling
  • 8 MULTIPLE TESTING
  • 8.1 Motivation
  • 8.2 Notation and Various Error Rates
  • 8.3 Single-step vs. Stepwise Methods
  • 8.4 Methods Based on Individual p-Values
  • 8.5 Resampling Methods Accounting for Dependence
  • References