Basics of Modern Mathematical Statistics

1. Front Matter

   Pages i-xviii

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2. Basic Notions

   • Vladimir Spokoiny, Thorsten Dickhaus

   Pages 1-10

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

   • Vladimir Spokoiny, Thorsten Dickhaus

   Pages 11-73

4. Regression Estimation

   • Vladimir Spokoiny, Thorsten Dickhaus

   Pages 75-118

5. Estimation in Linear Models

   • Vladimir Spokoiny, Thorsten Dickhaus

   Pages 119-172

6. Bayes Estimation

   • Vladimir Spokoiny, Thorsten Dickhaus

   Pages 173-194

7. Testing a Statistical Hypothesis

   • Vladimir Spokoiny, Thorsten Dickhaus

   Pages 195-222

8. Testing in Linear Models

   • Vladimir Spokoiny, Thorsten Dickhaus

   Pages 223-243

9. Some Other Testing Methods

   • Vladimir Spokoiny, Thorsten Dickhaus

   Pages 245-267

10. Back Matter

    Pages 269-296

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This textbook provides a unified and self-contained presentation of the main approaches to and ideas of mathematical statistics. It collects the basic mathematical ideas and tools needed as a basis for more serious study or even independent research in statistics. The majority of existing textbooks in mathematical statistics follow the classical asymptotic framework. Yet, as modern statistics has changed rapidly in recent years, new methods and approaches have appeared. The emphasis is on finite sample behavior, large parameter dimensions, and model misspecifications. The present book provides a fully self-contained introduction to the world of modern mathematical statistics, collecting the basic knowledge, concepts and findings needed for doing further research in the modern theoretical and applied statistics. This textbook is primarily intended for graduate and postdoc students and young researchers who are interested in modern statistical methods.

• Coverage and Concentration
• Estimators and Tests
• Exponential Family
• Linear Models
• Maximum Likelihood

• Weierstrass Institute (WIAS), Berlin, Germany

  Vladimir Spokoiny

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

  Thorsten Dickhaus

Vladimir Spokoiny defended his PhD at the Lomonosoff State University Moscow in 1988. Since 2000 he has been the head of the research group “Nonparametric Statistics” at the Weierstrass Institute Berlin, and since 2002 he has served as a professor of Statistics and Economics at the Humboldt University Berlin.

Thorsten Dickhaus received his Ph. D. from Heinrich-Heine-University Düsseldorf in 2008. After postdoc positions at the German Diabetes Center Düsseldorf and Berlin Institute of Technology, he became a junior professor of Mathematical Statistics at the Humboldt University Berlin in 2010.

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