Course in Large Sample Theory

ISBN-10: 0412043718
ISBN-13: 9780412043710
Edition: 1996
List price: $125.95 Buy it from $85.49
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Description: Presented in four parts, this book provides a complete picture of genome statistics. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as  More...

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Book details

List price: $125.95
Copyright year: 1996
Publisher: CRC Press LLC
Publication date: 7/1/1996
Binding: Paperback
Pages: 256
Size: 6.25" wide x 9.50" long x 0.50" tall
Weight: 0.748
Language: English

Presented in four parts, this book provides a complete picture of genome statistics. 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 ideal for 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, making it an ideal text for self study.

Preface
Basic Probability
Modes of Convergence
Partial Converses to Theorem 1
Convergence in Law
Laws of Large Numbers
Central Limit Theorems
Basic Statistical Large Sample Theory
Slutsky Theorems
Functions of the Sample Moments
The Sample Correlation Coefficient
Pearson's Chi-Square
Asymptotic Power of the Pearson Chi-Square Test
Special Topics
Stationary m-Dependent Sequences
Some Rank Statistics
Asymptotic Distribution of Sample Quantiles
Asymptotic Theory of Extreme Order Statistics
Asymptotic Joint Distributions of Extrema
Efficient Estimation and Testing
A Uniform Strong Law of Large Numbers
Strong Consistency of Maximum-Likelihood Estimates
Asymptotic Normality of the Maximum-Likelihood Estimate
The Cramer-Rao Lower Bound
Asymptotic Efficiency
Asymptotic Normality of Posterior Distributions
Asymptotic Distribution of the Likelihood Ratio Test Statistic
Minimum Chi-Square Estimates
General Chi-Square Tests
Appendix: Solutions to the exercises
References
Index

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