Statistical Tests of Nonparametric Hypotheses

Asymptotic Theory

An overview of the asymptotic theory of optimal nonparametric tests is presented in this book. It covers a wide range of topics: Neyman–Pearson and LeCam's theories of optimal tests, the theories of empirical processes and kernel estimators with extensions of their applications to the asymptotic behavior of tests for distribution functions, densities and curves of the nonparametric models defining the distributions of point processes and diffusions. With many new test statistics developed for smooth curves, the reliance on kernel estimators with bias corrections and the weak convergence of the estimators are useful to prove the asymptotic properties of the tests, extending the coverage to semiparametric models. They include tests built from continuously observed processes and observations with cumulative intervals.

Contents:

• Introduction
• Asymptotic Theory
• Nonparametric Tests for One Sample
• Two-Sample Tests
• Multi-Dimensional Tests
• Nonparametric Tests for Processes
• Nonparametric Tests Under Censoring or Truncation
• Sequential Tests

Readership: Researchers and graduates in the field of probability and statistics, and biomathematics.
Key Features:

• The book gives a survey of the theory and explains how to build optimal tests in statistics
• The asymptotic efficiency and the asymptotic equivalence of tests are carefully illustrated in the examples and exercises along with their corrections