Basics of Modern Mathematical Statistics

1. Front Matter

   Pages i-xxv

   PDF

2. Basics

   • Wolfgang Karl Härdle, Vladimir Spokoiny, Vladimir Panov, Weining Wang

   Pages 1-8

3. Parameter Estimation for an i.i.d. Model

   • Wolfgang Karl Härdle, Vladimir Spokoiny, Vladimir Panov, Weining Wang

   Pages 9-51

4. Parameter Estimation for a Regression Model

   • Wolfgang Karl Härdle, Vladimir Spokoiny, Vladimir Panov, Weining Wang

   Pages 53-72

5. Estimation in Linear Models

   • Wolfgang Karl Härdle, Vladimir Spokoiny, Vladimir Panov, Weining Wang

   Pages 73-106

6. Bayes Estimation

   • Wolfgang Karl Härdle, Vladimir Spokoiny, Vladimir Panov, Weining Wang

   Pages 107-128

7. Testing a Statistical Hypothesis

   • Wolfgang Karl Härdle, Vladimir Spokoiny, Vladimir Panov, Weining Wang

   Pages 129-158

8. Testing in Linear Models

   • Wolfgang Karl Härdle, Vladimir Spokoiny, Vladimir Panov, Weining Wang

   Pages 159-166

9. Some Other Testing Methods

   • Wolfgang Karl Härdle, Vladimir Spokoiny, Vladimir Panov, Weining Wang

   Pages 167-182

10. Back Matter

    Pages 183-185

    PDF

​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.

• Bayes estimation
• Modern statistics
• Parameter estimation
• Regression
• Statistical tests

From the reviews:

“The book ‘Basics of model mathematical statistics’ is built as a series of focused exercises revolving around parameter estimation, linear models, Bayesian estimation and statistical hypothesis testing. … This book is a valuable resource for undergraduates and post-graduates alike. The detailed proofs and the R code and output make it a must have for the understanding of modern mathematical statistics.” (Irina Ioana Mohorianu, zbMATH, Vol. 1286 (1), 2014)

• C.A.S.E. Centre f. Appl. Stat. & Econ. School of Business and Economics, Humboldt-Universität zu Berlin L.v.Bortkiewicz Chair of Statistics, Berlin, Germany

  Wolfgang Karl Härdle

• Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Berlin, Germany

  Vladimir Spokoiny

• Universität Duisburg-Essen, Essen, Germany

  Vladimir Panov

• Chair of Statistics C.A.S.E. Center for Applied Statistics & Economics, Humboldt University at Berlin Ladislaus von Bortkiewicz, Berlin, Germany

  Weining Wang

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.

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