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Approximate Distributions of Order Statistics - With Applications to Nonparametric Statistics (Hardcover, 1989 ed.)
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Approximate Distributions of Order Statistics - With Applications to Nonparametric Statistics (Hardcover, 1989 ed.)
Rolf-Dieter Reiss
Series: Springer Series in Statistics
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This book is designed as a unified and mathematically rigorous
treatment of some recent developments of the asymptotic
distribution theory of order statistics (including the extreme
order statistics) which are relevant for statistical theory and its
applications. Particular emphasis is placed on results concerning
the accuracy of limit theorems, on higher order approximations and
other approximations in quite a general sense. Contrary to the
classical limit theorems, that primarily concern the weak
convergence of distribution functions, our main results will be
formulated in terms of the variational and the Hellinger distance.
These results will form the proper springboard for the
investigation of parametric approximations of nonparametric models
of joint distributions of order statistics. The approximating
models include normal as well as extreme value models. Several
applications will show the usefulness of this approach. This book
is intended for students and research workers in probability and
statistics, and practitioners involved in applications of
mathematical results conderning order statistics and extremes. The
knowledge of calculus and topics that are taught in introductory
probability and statistic courses are necessary for the
understanding of this book.
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