Distributions of Goodness-Of-Fit Statistics

By Gennady Martynov

This book is devoted to the theory of goodness-of-fit tests basedon weighted empirical processes. Much attention has been given tothe limit distributions of statistics of these tests as well as toconvergence problems. Cram r-von Mises statistics are studiedthroughout most of the book, but attention is also given to theKolmogorov-Smirnov test, the chi-square goodness-of-fit test aswell as some others.

The authors describe statistics to test simple and complexparametric hypotheses. Other hypotheses are also be considered, namely the hypothesis of distributional symmetry, the hypothesis ofuniformity for random variables on a circle, the hypothesis ofuniformity of distribution on a multidimensional cube, and thehypothesis of independence of the components of multidimensionalvectors. Tests based on the transformed empirical process are alsodiscussed. The expressions for eigenvalues and eigenfunctions arederived for many covariance operators corresponding to variousempirical processes. The resulting eigenfunctions are oftenexpressed in terms of known special functions.
Methods for computing the distribution of various types ofquadratic form from normal random variables are also described.These methods are not well known in the literature. Thetheory is accompanied by a collection of small tables ofdistributions, and in some cases by small programs in theMATHEMATICA language. All tables of quantiles for theCram r-von Mises tests have been computed by exact numericalmethods. Some tables of distributions of the similarKolmogorov-Smirnov statistics, once again found using simulations, are also included in this book.

• Format: Hardcover
• Language: English
• ISBN: 1848216017
• ISBN13: 9781848216013
• Release Date: June 2023
• Publisher: Wiley-Iste
• Length: 368 Pages