Contiguity of Probability Measures: Some Applications in Statistics – A Foundational Work on Asymptotic Theory by George

Introduction

For advanced students and researchers in statistics and probability theory, the concept of 'contiguity' of probability measures offers a refined lens through which to view large-sample behaviour. George G. Roussas's Contiguity of Probability Measures: Some Applications in Statistics is a seminal work that systematically unpacks this powerful mathematical tool. Originally published by Cambridge University Press, this hardbound edition is an essential reference for those delving into asymptotic statistics, providing both theoretical depth and practical applications. This book is particularly valuable for Indian scholars and professionals engaged in rigorous statistical research and teaching.

Book Overview

This monograph provides the first systematic treatment of contiguity—a concept that describes the 'nearness' of sequences of probability measures. Roussas begins by defining contiguity and relating it to more familiar ideas such as absolute continuity and mutual singularity. He then proceeds to establish a series of general theorems that form the backbone of the theory. The book culminates in a detailed discussion of applications, including asymptotic expansions and the distribution of likelihood functions, making it an indispensable resource for anyone working in large-sample theory. The text is rigorous yet accessible to those with a solid grounding in measure-theoretic probability.

Key Highlights

• First Systematic Exposition: The book offers the first comprehensive and structured discussion of contiguity in the existing literature.
• Rigorous Theorems: Includes detailed proofs of general theorems that are foundational for asymptotic statistics.
• Practical Applications: Demonstrates how contiguity simplifies derivations in large-sample theory, particularly in likelihood-based inference.
• Authoritative Source: Written by George G. Roussas, a renowned statistician known for his contributions to probability and statistical theory.
• Classic Reference: A timeless addition to any academic library, published by the prestigious Cambridge University Press.

Inside the Book

The book is structured to build from fundamental concepts to advanced applications. Early chapters introduce the notion of contiguity and provide alternative characterizations, linking it to concepts like Hellinger distance and Kullback-Leibler divergence. The middle sections are dedicated to proving key theorems, including those on the asymptotic behaviour of likelihood ratios and the contiguity of product measures. The final chapters apply these results to real statistical problems, such as deriving asymptotic distributions of test statistics and establishing optimality properties of estimators. The logical flow ensures that readers develop a deep, working understanding of the material.

Key Topics

• Definition and characterizations of contiguity
• Relationship with absolute continuity and singularity
• Asymptotic expansions of likelihood functions
• Contiguity and the central limit theorem
• Applications in hypothesis testing and estimation
• Large-sample properties of maximum likelihood estimators
• Asymptotic distribution of likelihood ratio statistics

Reader Benefits

• Deepen Theoretical Understanding: Gain a thorough grasp of a sophisticated concept that is often glossed over in standard texts.
• Simplify Complex Derivations: Learn how contiguity can streamline proofs and derivations in large-sample theory, saving time and effort.
• Enhance Research Capability: Equip yourself with a tool that opens doors to advanced research in statistics and probability.
• Strengthen Academic Foundation: Ideal for preparing for qualifying exams or teaching advanced courses in statistical inference.
• Access a Classic Text: Own a hardcover copy of a foundational work that remains relevant decades after its first publication.

Learning Outcomes

By studying this book, readers will be able to: (1) define and characterize contiguity for sequences of probability measures; (2) relate contiguity to other measure-theoretic concepts; (3) prove and apply key theorems involving contiguity; (4) derive asymptotic expansions of likelihood functions under contiguous alternatives; and (5) apply contiguity to solve problems in hypothesis testing and estimation within a large-sample framework. These outcomes are essential for anyone pursuing a PhD in statistics or a related field.

Who Should Read

• Graduate Students: In statistics, mathematics, or econometrics who are taking advanced courses in probability and inference.
• Academic Researchers: Working in asymptotic theory, nonparametric statistics, or high-dimensional inference.
• Professional Statisticians: Who need a rigorous reference for large-sample methods.
• Instructors: Teaching courses on advanced statistical theory or probability measures.
• Libraries: University and institutional libraries that serve mathematics and statistics departments.

About the Author

George G. Roussas is a distinguished professor and researcher in the field of statistics. He has made significant contributions to probability theory, statistical inference, and the theory of contiguity. With a career spanning several decades, he has authored numerous influential papers and books. His clear exposition and rigorous approach have made his works standard references for advanced students and researchers worldwide. Professor Roussas's deep understanding of the subject shines through every page of this monograph.

About the Publisher

Cambridge University Press is one of the oldest and most respected academic publishers in the world. Known for its commitment to scholarly excellence, Cambridge University Press publishes works that set the standard in their fields. This hardcover edition of Contiguity of Probability Measures upholds that tradition, offering a durable and beautifully printed volume that will withstand years of use in a library or personal collection. For Indian readers, this book represents a direct link to the highest quality of international academic publishing.

Conclusion

Contiguity of Probability Measures: Some Applications in Statistics by George G. Roussas is more than just a book—it is a key that unlocks a deeper understanding of asymptotic statistics. Whether you are a graduate student grappling with large-sample theory or a seasoned researcher seeking a reliable reference, this hardcover edition is a worthy investment. Its systematic approach, rigorous proofs, and practical applications make it a timeless classic. Order your copy today from Bookshops.in and add this essential volume to your academic collection.