Some Limit Theorems in Statistics

R. Bahadur9780898711752, 0898711754

A discussion of some topics in the theory of large deviations such as moment-generating functions and Chernoff’s theorem, and of aspects of estimation and testing in large samples, such as exact slopes of test statistics.

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Table of contents :
Some Limit Theorems in Statistics……Page 1
Contents……Page 5
Preface……Page 7
1. Introduction…….Page 9
2. Moment generating functions…….Page 10
3. Chernoff’s theorem…….Page 14
4. The Kullback-Leibler information number…….Page 17
5. Some examples of large deviation probabilities…….Page 21
6. Stein’s lemma. Asymptotic effective variances…….Page 27
7. Exact slopes of test statistics…….Page 34
8. Some examples of exact slopes…….Page 38
9. The existence and consistency of maximum likelihood estimates…….Page 40
10. The exact slope of the likelihood ratio statistic…….Page 45
REFERENCES……Page 49