From Finite Sample to Asymptotic Methods in Statistics: (Series Number 29 Cambridge Series in Statistical and Probabilistic Mathematics)

Exact statistical inference may be employed in diverse fields of science and technology. As problems become more complex and sample sizes become larger, mathematical and computational difficulties can arise that require the use of approximate statistical methods. Such methods are justified by asymptotic arguments but are still based on the concepts and principles that underlie exact statistical inference. With this in perspective, this book presents a broad view of exact statistical inference and the development of asymptotic statistical inference, providing a justification for the use of asymptotic methods for large samples. Methodological results are developed on a concrete and yet rigorous mathematical level and are applied to a variety of problems that include categorical data, regression, and survival analyses. This book is designed as a textbook for advanced undergraduate or beginning graduate students in statistics, biostatistics, or applied statistics but may also be used as a reference for academic researchers.

Table of Contents:
1. Motivation and basic tools; 2. Estimation theory; 3. Hypothesis testing; 4. Elements of statistical decision theory; 5. Stochastic processes: an overview; 6. Stochastic convergence and probability inequalities; 7. Asymptotic distributions; 8. Asymptotic behavior of estimators and tests; 9. Categorical data models; 10. Regression models; 11. Weak convergence and Gaussian processes.

About the Author :
Pranab K. Sen is the Cary C. Boshamer Professor of Biostatistics and Professor of Statistics and Operations Research at the University of North Carolina, Chapel Hill. He is the author or co-author of numerous textbooks in statistics and biostatistics, and editor or co-editor of numerous volumes in the same field. He has more than 600 publications in leading statistics journals and has supervised 83 doctoral students. Sen is a Fellow of both the Institute of Mathematical Statistics and the American Statistical Association. In 2002 he was Senior Noether Awardee for his lifelong contributions to nonparametrics and received the Commemoration Medal from the Czech Union of Physicists and Mathematicians in 1998. Julio M. Singer is a Professor at the Department of Statistics, University of São Paulo, Brazil, and is the co-director of the university's Center for Applied Statistics. Professor Singer is the co-author of books on categorical data and large sample theory and has publications in both methodological and applications-oriented journals. He was the 1993 James E. Grizzle Distinguished Alumnus in Biostatistics from the University of North Carolina at Chapel Hill. He supervised several graduate students and contributed to the development of the doctoral program in statistics at the University of São Paulo, Brazil. Antonio C. Pedroso-de-Lima is an Associate Professor at the Department of Statistics, University of São Paulo, Brazil, and is the co-director of the university's Center for Applied Statistics. He received his doctoral degree in biostatistics from the University of North Carolina at Chapel Hill. He is the co-author of a book on introductory statistics, and his research has been published in theoretical, methodological, and applications-oriented journals. Professor Pedroso-de-Lima has advised a number of master's degree and doctoral students in the graduate program in statistics at the University of São Paulo.