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Nonparametric Monte Carlo tests and their applications. (English) Zbl 1094.62058
Lecture Notes in Statistics 182. New York, NY: Springer (ISBN 0-387-25038-7/pbk). xi, 181 p. (2005).
Nonparametric Monte Carlo tests (NMCT) are more and more used everywhere when standard theory fails, being the main reason why they are more and more popular. The author of this concise monograph shows several fields where NMCT procedures can be effectively used, e.g.:
testing for multivariate distributions; asymptotics of goodness-of-fit tests; dimension reduction for regression; checking the adequacy of partial linear models; model checking for multivariate regression models; heteroscedasticity tests for regression; checking the adequacy of a varying coefficients model; homogeneity testing for covariance matrices.
The connection to the bootstrap is also shortly discussed. The book is based on recently published papers of the author, being a co-author of almost 20 papers from the field, most of them previously reviewed in Zentralblatt. I recommend the book not only to the everybody who is deeply interested in Monte Carlo simulations but also to those interested in asymptotics and bootstrap.

MSC:
62G10 Nonparametric hypothesis testing
62C05 General considerations in statistical decision theory
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62G09 Nonparametric statistical resampling methods
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