Nonparametric Inference

This book provides a comprehensive and balanced treatment of both classical and modern methods in nonparametric inference. It begins with foundational topics such as order statistics, ranks, and confidence intervals for medians and percentiles, before progressing to distribution-free tests, robust estimators, regression quantiles, and U-statistics. Advanced topics include nonparametric density and regression estimation, model diagnostics, empirical likelihood, and survival analysis, including nonparametric Bayesian and maximum likelihood estimators. The book uniquely integrates these topics into a single resource, making it distinct from other texts in the field.

Key Features:

• A balanced blend of classical methods (e.g., rank and sign tests) and modern techniques (e.g., bootstrap, empirical likelihood, and nonparametric regression)
• Comprehensive coverage of nonparametric density and regression estimation, model diagnostics, and survival analysis, including Bayesian and maximum likelihood approaches
• Unique inclusion of empirical likelihood inference, a broadly applicable and essential methodology for contemporary graduate courses
• Numerous exercises and notes at the end of chapters to reinforce concepts and provide historical context
• Designed for both teaching and reference, offering up-to-date techniques in nonparametric inference

This text is ideal for a two-semester course on nonparametric inference for graduate students in statistics, applied mathematics, machine learning, and computer science. It also serves as a valuable reference for researchers and practitioners interested in nonparametric methods. Its comprehensive scope, including empirical likelihood, nonparametric Bayes, and bootstrap methodologies, makes it a unique resource. Notes at the end of each chapter provide insights into the chronological development of the field, while numerous exercises help reinforce the concepts and methodologies presented.

Hira L. Koul secured his doctorate in statistics from the University of California, Berkeley in 1967. He joined the Department of Statistics and Probability, Michigan State University (MSU) on January 1, 1968. Since January 1, 2018, he has been Professor Emeritus at the MSU, after serving there as a faculty member for 50 years. His areas of research include nonparametric inference, inference on short and long memory processes, time series analysis and survival analysis. He has published around 150 papers, several monographs and books and guided 35 doctoral theses. He is a Fellow of the American Statistical Association and of the Institute of Mathematical Statistics and Past President of the International Indian Statistical Association. He was a recipient of a Humboldt Research Award for senior scientists in October 1995 and a Distinguished Faculty Award at the MSU, 2005.

Anton Schick earned his doctorate in statistics from Michigan State University in 1983. He spent one year at Tufts University before joining the Department of Mathematical Sciences at Binghamton University in the fall of 1984. He retired as full professor on September 1, 2024 after forty years of service that included two terms as chair. His research has focused on the characterization and construction of efficient statistical inference procedures in nonparametric and semiparametric models with an emphasis on regression and time series models, on curve estimation with parametric rates, on inference with incomplete data, and on the empirical likelihood approach. He has published one hundred twenty research papers and guided ten doctoral theses.

Palaniappan Vellaisamy is currently a Visiting Professor in the Department of Statistics and Applied Probability, University of California, Santa Barbara, USA. He completed his Ph.D. degree in statistics from Indian Institute of Technology Kanpur in 1989. He worked as a Research Associate from July 1989 to December 1990 at the Indian Statistical Institute, New Delhi. Then he joined in 1991 as an Assistant Professor in the Department of Mathematics at Indian Institute of Technology Bombay, India. He became a full professor in 2003 and retired in June 2024. His research areas include statistical inference, applied probability, and fractional stochastic processes. He has published more than 120 research papers in various journals of statistics and probability and has guided 11 Ph.D.’s. He is currently an Associate Editor for Statistics and Probability Letters and The Journal of Indian Statistical Association.