Hardcover ISBN:  9780821852835 
Product Code:  GSM/119 
246 pp 
List Price:  $72.00 
MAA Member Price:  $64.80 
AMS Member Price:  $57.60 
Electronic ISBN:  9781470415938 
Product Code:  GSM/119.E 
246 pp 
List Price:  $67.00 
MAA Member Price:  $60.30 
AMS Member Price:  $53.60 

Book DetailsGraduate Studies in MathematicsVolume: 119; 2011MSC: Primary 62;
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 largesample 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 graduatelevel courses in probability and statistics.ReadershipGraduate students and research mathematicians interested in mathematical statistics.

Table of Contents

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. Changepoint 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


Additional Material

Reviews

This is a well written book and should be of great interest to advanced graduate students/researchers in mathematical statistics. The material is presented with great clarity by using simple models as opposed to complex ones. ... Overall it should be of great value to advanced graduate students and researchers in theoretical statistics. The book can be recommended for libraries on campuses with a graduate program in statistics.
Mathematical Reviews


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 Book Details
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 Get Permissions
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 largesample 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 graduatelevel courses in probability and statistics.
Graduate students and research mathematicians interested in mathematical statistics.

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. Changepoint 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

This is a well written book and should be of great interest to advanced graduate students/researchers in mathematical statistics. The material is presented with great clarity by using simple models as opposed to complex ones. ... Overall it should be of great value to advanced graduate students and researchers in theoretical statistics. The book can be recommended for libraries on campuses with a graduate program in statistics.
Mathematical Reviews