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Mathematical Statistics: Asymptotic Minimax Theory

About this Title

Alexander Korostelev, Wayne State University, Detroit, MI and Olga Korosteleva, California State University, Long Beach, CA

Publication: Graduate Studies in Mathematics
Publication Year: 2011; Volume 119
ISBNs: 978-0-8218-5283-5 (print); 978-1-4704-1593-8 (online)
DOI: https://doi.org/10.1090/gsm/119
MathSciNet review: MR2767163
MSC: Primary 62-01; Secondary 62C20, 62E20, 62Fxx, 62Gxx, 62Lxx

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Table of Contents

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Front/Back Matter

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Part 1. Parametric models

• 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

Part 2. Nonparametric 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

Part 3. Estimation in nonparametric models

• Chapter 13. Estimation of functionals
• Chapter 14. Dimension and structure in nonparametric regression
• Chapter 15. Adaptive estimation
• Chapter 16. Testing of nonparametric hypotheses