Mathematical Statistics: Asymptotic Minimax Theory (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 119)

This book is designed to bridge the gap between traditional textbooks in statistics and more advanced books that include the sophisticated nonparametric techniques. It covers topics in parametric and nonparametric large-sample estimation theory. The exposition is based on a collection of relatively simple statistical models. It gives a thorough mathematical analysis for each of them with all the rigorous proofs and explanations. The book also includes a number of helpful exercises. Prerequisites for the book include senior undergraduate/beginning graduate-level courses in probability and statistics. Readership: Graduate students and research mathematicians interested in mathematical statistics Chapter 1. The Fisher Efficiency Chapter 2. The Bayes And Minimax Estimators Chapter 3. Asymptotic Minimaxity Chapter 4. Some Irregular Statistical Experiments Chapter 5. Change-point Problem Chapter 6. Sequential Estimators Chapter 7. Linear Parametric Regression Chapter 8. Estimation In Nonparametric Regression Chapter 9. Local Polynomial Approximation Of Regression Function Chapter 10. Estimation Of Regression In Global Norms Chapter 11. Estimation By Splines Chapter 12. Asymptotic Optimality In Global Norms Chapter 13. Estimation Of Functionals Chapter 14. Dimension And Structure In Nonparametric Regression Chapter 15. Adaptive Estimation Chapter 16. Testing Of Nonparametric Hypotheses Alexander Korostelev, Olga Korosteleva. Includes Bibliographical References (p. 239) And Indexes. "This book is designed to bridge the gap between traditional textbooks in statistics and more advanced books that include the sophisticated nonparametric techniques. It covers topics in parametric and nonparametric large-sample estimation theory. The exposition is based on a collection of relatively simple statistical models. It gives a thorough mathematical analysis for each of them with all the rigorous proofs and explanations. The book also includes a number of helpful exercises."--Publisher's description