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Full Description
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.
Contents
1 Introduction. 3 Order Statistics and Ranks. 4 Testing of Hypotheses in Location Models. 5 U-Statistics. 6 Estimation in Location Models. 7 Density Estimation. 8 Nonparametric Regression. 9 Model Diagnostics. 10 Empirical Likelihood. 11 Survival Analysis. 12 Bibliography.
