Basics of Modern Mathematical Statistics

This book presents numerous exercises with solutions to help the reader better understand different aspects of modern statistics. It features applications with R and Matlab code that show how to practically use the methods.

The complexity of today's statistical data calls for modern mathematical tools. Many fields of science make use of mathematical statistics and require continuous updating on statistical technologies. Practice makes perfect, since mastering the tools makes them applicable. Our book of exercises and solutions offers a wide range of applications and numerical solutions based on R.
In modern mathematical statistics, the purpose is to provide statistics students with a number of basic exercises and also an understanding of how the theory can be applied to real-world problems.
The application aspect is also quite important, as most previous exercise books are mostly on theoretical derivations. Also we add some problems from topics often encountered in recent research papers.
The book was written for statistics students with one or two years of coursework in mathematical statistics and probability, professors who hold courses in mathematical statistics, and researchers in other fields who would like to do some exercises on math statistics.

Autorentext

Wolfgang Karl Härdle is Professor of Statistics at the Humboldt-Universität zu Berlin and the Director of CASE the Centre for Applied Statistics and Economics. He teaches quantitative finance and semi-parametric statistical methods. His research focuses on dynamic factor models, multivariate statistics in finance and computational statistics. He is an elected member of the ISI and an advisor to the Guanghua School of Management, Peking University and to National Central University, Taiwan.

Vladimir Panov is a postdoctoral researcher at the University of Duisburg-Essen. His research interests include statistical inference on stochastic processes, especially on models based on Levy processes. Over the last several years he has worked as a research assistant at the Weierstrass Institute for Applied Analysis and Stochastics (Berlin), where he has focused on multidimensional statistical models.

Vladimir Spokoiny is a Professor at the Humboldt University of Berlin and focuses on applicable mathematical statistics. Weining Wang is a postdoctoral researcher at CASE the Centre for Applied Statistics and Economics, where she teaches quantitative finance and semi-parametric statistical methods. Her research focuses on quantile regression and high-dimensional nonparametric models.

Weining Wang is a postdoctoral researcher at CASE the Centre for Applied Statistics and Economics, where she teaches quantitative finance and semi-parametric statistical methods. Her research focuses on quantile regression and high-dimensional nonparametric models.

Inhalt
Basics.- Parameter Estimation for an i.i.d. Model.- Parameter Estimation for a Regression Model.- Estimation in Linear Models.- Bayes Estimation.- Testing a Statistical Hypothesis.- Testing in Linear Models.- Some Other Testing Methods.