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An Introduction to Nonparametric Statistics presents techniques for
statistical analysis in the absence of strong assumptions about the
distributions generating the data. Rank-based and resampling
techniques are heavily represented, but robust techniques are
considered as well. These techniques include one-sample testing and
estimation, multi-sample testing and estimation, and regression.
Attention is paid to the intellectual development of the field,
with a thorough review of bibliographical references. Computational
tools, in R and SAS, are developed and illustrated via examples.
Exercises designed to reinforce examples are included. Features
Rank-based techniques including sign, Kruskal-Wallis, Friedman,
Mann-Whitney and Wilcoxon tests are presented Tests are inverted to
produce estimates and confidence intervals Multivariate tests are
explored Techniques reflecting the dependence of a response
variable on explanatory variables are presented Density estimation
is explored The bootstrap and jackknife are discussed This text is
intended for a graduate student in applied statistics. The course
is best taken after an introductory course in statistical
methodology, elementary probability, and regression. Mathematical
prerequisites include calculus through multivariate differentiation
and integration, and, ideally, a course in matrix algebra.
This book presents theoretical results relevant to Edgeworth and
saddlepoint expansions to densities and distribution functions. It
provides examples of their application in some simple and a few
complicated settings, along with numerical, as well as asymptotic,
assessments of their accuracy. Variants on these expansions,
including much of modern likelihood theory, are discussed and
applications to lattice distributions are extensively treated. This
book is intended primarily for advanced graduate students and
researchers in the field needing a collection of core results in a
uniform notation, with bibliographical references to further
examples and applications. It assumes familiarity with real
analysis, vector calculus, and complex analysis. This third edition
features an expansion of the material on the Blackwell
approximation and an expansion of the discussions on saddlepoint
approximation. John E. Kolassa is Assistant Professor of
Biostatistics at the University of Rochester.
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