Mathematical Statistics

This book requires knowledge of probability theory (combinatorics, probability distributions, functions and sequences of random variables) which is typically taught in the earlier semesters of scientific and mathematical study courses. After the basic ideas of mathematical statistics, Mathematical Statistics gives an introduction to point estimation, confidence intervals and statistical tests. Based on the general theory of linear models, the book provides an in-depth overview of the following: Analysis of variance for models with fixed, random and mixed effects Regression analysis is also first presented for linear models with fixed, random and mixed effects before being expanded to nonlinear models. Statistical multi-decision problems like statistical selection procedures (Bechhofer and Gupta) and sequential tests Design of experiments from a mathematical-statistical point of view. The chapters also contain exercises with hints for solutions.