Theory of Nonparametric Tests

ISBN-13: 9783319763149 / Angielski / Twarda / 2018 / 124 str.

Thorsten Dickhaus

Opis

This textbook provides a self-contained presentation of the main concepts and methods of nonparametric statistical testing, with a particular focus on the theoretical foundations of goodness-of-fit tests, rank tests, resampling tests, and projection tests.

Spis treści

Introduction and Examples.- Empirical Measure, Empirical Processes.- Goodness-of-fit Tests.- Rank Tests.- Asymptotics of Linear Resampling Statistics.- Bootstrap Methods for Linear Models.- Projection Tests.- Some Extensions.

O autorze

Thorsten Dickhaus obtained his Ph.D. in mathematics from the Heinrich Heine University, Düsseldorf, Germany in 2008. He held postdoc positions at the German Diabetes Center Düsseldorf and Berlin Institute of Technology. In 2010 he became a Junior Professor of Mathematical Statistics at the Humboldt University of Berlin, Germany. Since 2015 he has been a Full Professor of Mathematical Statistics at the University of Bremen, Germany.

Blurb

This textbook provides a self-contained presentation of the main concepts and methods of nonparametric statistical testing, with a particular focus on the theoretical foundations of goodness-of-fit tests, rank tests, resampling tests, and projection tests. The substitution principle is employed as a unified approach to the nonparametric test problems discussed. In addition to mathematical theory, it also includes numerous examples and computer implementations. The book is intended for advanced undergraduate, graduate, and postdoc students as well as young researchers. Readers should be familiar with the basic concepts of mathematical statistics typically covered in introductory statistics courses.