Hira L. Koul - Böcker

The role of the weak convergence technique via weighted empirical processes has proved to be very useful in advancing the development of the asymptotic theory of the so called robust inference procedures corresponding to non-smooth score functions from linear models to nonlinear dynamic models in the 1990's. This monograph is an ex­ panded version of the monograph Weighted Empiricals and Linear Models, IMS Lecture Notes-Monograph, 21 published in 1992, that includes some aspects of this development. The new inclusions are as follows. Theorems 2. 2. 4 and 2. 2. 5 give an extension of the Theorem 2. 2. 3 (old Theorem 2. 2b. 1) to the unbounded random weights case. These results are found useful in Chapters 7 and 8 when dealing with ho­ moscedastic and conditionally heteroscedastic autoregressive models, actively researched family of dynamic models in time series analysis in the 1990's. The weak convergence results pertaining to the partial sum process given in Theorems 2. 2. 6 . and 2. 2. 7 are found useful in fitting a parametric autoregressive model as is expounded in Section 7. 7 in some detail. Section 6. 6 discusses the related problem of fit­ ting a regression model, using a certain partial sum process. Inboth sections a certain transform of the underlying process is shown to provide asymptotically distribution free tests. Other important changes are as follows. Theorem 7. 3.

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 approachesUnique inclusion of empirical likelihood inference, a broadly applicable and essential methodology for contemporary graduate coursesNumerous exercises and notes at the end of chapters to reinforce concepts and provide historical contextDesigned for both teaching and reference, offering up-to-date techniques in nonparametric inferenceThis 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.

Box and Jenkins (1970) made the idea of obtaining a stationary time series by differencing the given, possibly nonstationary, time series popular. Numerous time series in economics are found to have this property. Subsequently, Granger and Joyeux (1980) and Hosking (1981) found examples of time series whose fractional difference becomes a short memory process, in particular, a white noise, while the initial series has unbounded spectral density at the origin, i.e. exhibits long memory.Further examples of data following long memory were found in hydrology and in network traffic data while in finance the phenomenon of strong dependence was established by dramatic empirical success of long memory processes in modeling the volatility of the asset prices and power transforms of stock market returns.At present there is a need for a text from where an interested reader can methodically learn about some basic asymptotic theory and techniques found useful in the analysis of statistical inference procedures for long memory processes. This text makes an attempt in this direction. The authors provide in a concise style a text at the graduate level summarizing theoretical developments both for short and long memory processes and their applications to statistics. The book also contains some real data applications and mentions some unsolved inference problems for interested researchers in the field.

During the last two decades, many areas of statistical inference have experienced phenomenal growth. This book presents a timely analysis and overview of some of these new developments and a contemporary outlook on the various frontiers of statistics.Eminent leaders in the field have contributed 16 review articles and 6 research articles covering areas including semi-parametric models, data analytical nonparametric methods, statistical learning, network tomography, longitudinal data analysis, financial econometrics, time series, bootstrap and other re-sampling methodologies, statistical computing, generalized nonlinear regression and mixed effects models, martingale transform tests for model diagnostics, robust multivariate analysis, single index models and wavelets.This volume is dedicated to Prof. Peter J Bickel in honor of his 65th birthday. The first article of this volume summarizes some of Prof. Bickel's distinguished contributions.