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Course in Large Sample Theory [Kietas viršelis]

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A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.

The book is intended as a first year graduate course in large sample theory for statisticians. It has been used by graduate students in statistics, biostatistics, mathematics, and related fields. Throughout the book there are many examples and exercises with solutions. It is an ideal text for self study.
Preface vii
Part 1 Basic Probability
1(36)
1 Modes of Convergence
3(5)
2 Partial Converses to Theorem 1
8(5)
3 Convergence in Law
13(6)
4 Laws of Large Numbers
19(7)
5 Central Limit Theorems
26(11)
Part 2 Basic Statistical Large Sample Theory
37(30)
6 Slutsky Theorems
39(5)
7 Functions of the Sample Moments
44(7)
8 The Sample Correlation Coefficient
51(5)
9 Pearson's Chi-Square
56(5)
10 Asymptotic Power of the Pearson Chi-Square Test
61(6)
Part 3 Special Topics
67(38)
11 Stationary m-Dependent Sequences
69(6)
12 Some Rank Statistics
75(12)
13 Asymptotic Distribution of Sample Quantiles
87(7)
14 Asymptotic Theory of Extreme Order Statistics
94(7)
15 Asymptotic Joint Distributions of Extrema
101(4)
Part 4 Efficient Estimation and Testing
105(67)
16 A Uniform Strong Law of Large Numbers
107(5)
17 Strong Consistency of Maximum-Likelihood Estimates
112(7)
18 Asymptotic Normality of the Maximum-Likelihood Estimate
119(7)
19 The Cramer-Rao Lower Bound
126(7)
20 Asymptotic Efficiency
133(7)
21 Asymptotic Normality of Posterior Distributions
140(4)
22 Asymptotic Distribution of the Likelihood Ratio Test Statistic
144(7)
23 Minimum Chi-Square Estimates
151(12)
24 General Chi-Square Tests
163(9)
Appendix: Solutions to the exercises 172(64)
References 236(3)
Index 239
Thomas S. Ferguson