Bootstrap Methods

This book provides a compact introduction to the bootstrap method. In addition to classical results on point estimation and test theory, multivariate linear regression models and generalized linear models are covered in detail. Special attention is given to the use of bootstrap procedures to perform goodness-of-fit tests to validate model or distributional assumptions. In some cases, new methods are presented here for the first time.

The text is motivated by practical examples and the implementations of the corresponding algorithms are always given directly in R in a comprehensible form. Overall, R is given great importance throughout. Each chapter includes a section of exercises and, for the more mathematically inclined readers, concludes with rigorous proofs. The intended audience is graduate students who already have a prior knowledge of probability theory and mathematical statistics.

• Bootstrap based tests
• Regression analysis
• Survival analysis
• Longitudinal data analyis
• Experimental design
• Goodness of fit test
• Generalized Linear Models

• Department of Medical Engineering and Technomathemathics, FH Aachen – University of Applied Sciences, Jülich, Germany

  Gerhard Dikta

• Bayer AG, Cologne, Germany

  Marsel Scheer

Gerhard Dikta has been a full-time professor at the Department of Medical Engineering and Technomathematics within the University of Applied Sciences, FH-Aachen, since 1993. He has also been an adjunct professor at the Department of Mathematics of the University of Wisconsin-Milwaukee since 2004. In addition to general problems in mathematical statistics, statistical modeling, simulation and optimization, his research interests and contributions are in survival analysis and, recently, in the development of statistical test methods for model verification.

Marsel Scheer has been a data scientist at Bayer AG since 2019. He was head of biostatistics and software development at Myriad International GmbH (formerly Sividon Diagnostics GmbH) for 5 years and worked as a biometrician in diabetes research at the German Diabetes Center for 6 years. His research interests are in statistical learning and modeling, machine learning, simulation and software development.