Robust Rank-Based and Nonparametric Methods

The contributors to this volume include many of the distinguished researchers in this area. Many of these scholars have collaborated with Joseph McKean to develop underlying theory for these methods, obtain small sample corrections, and develop efficient algorithms for their computation. The papers cover the scope of the area, including robust nonparametric rank-based procedures through Bayesian and big data rank-based analyses. Areas of application include biostatistics and spatial areas. Over the last 30 years, robust rank-based and nonparametric methods have developed considerably. These procedures generalize traditional Wilcoxon-type methods for one- and two-sample location problems. Research into these procedures has culminated in complete analyses for many of the models used in practice including linear, generalized linear, mixed, and nonlinear models. Settings are both multivariate and univariate. With the development of R packages in these areas, computation of these procedures is easily shared with readers and implemented. This book is developed from the International Conference on Robust Rank-Based and Nonparametric Methods, held at Western Michigan University in April 2015.

• Includes theoretical research, novel applications of the methods, and research in computational procedures for these methods
• Topics span robust rank-based procedures for current models, like general linear models and cluster correlated models; robust rank-based multivariate methods, including affine invariant procedures; robust procedures for spatial analyses; and robust rank-based Bayesian procedures
• Includes implementation in R packages where possible

Autorentext

Dr. Regina Liu is currently Distinguished Professor of Statistics at Rutgers University, USA. She received her Ph.D. from Columbia University at New York. She has published extensively in a broad range of research areas, including nonparametric statistics, data depth, robust statistics, resampling techniques, text mining, fusion learning, statistical quality control, and aviation risk management. She has served on the editorial board of several statistical journals, including The Annals of Statistics, Journal of American Statistical Association, and Journal of Multivariate Analysis. She is the recipient of the 2011 Stieltjes Professor, Thomas Stieltjes Institute for Mathematics, the Netherlands. She has been elected fellow of American Statistical Association, Institute of Mathematical Statistics, and International Statistical Institute. Dr. Joseph McKean is Professor of Statistics at Western Michigan University. He received hisPhD in Statistics in 1975 from the Pennsylvania State University under the direction of Professor T.P. Hettmansperger. He has held several visiting research professorships at University of New South Wales. In 1999, he was elected as a fellow of the American Statistical Association. In 1994, he received the Distinguished Faculty Scholar Award from Western Michigan University. He served as Chair of the Nonparametric Section of the American Statistical Association during 2002. Dr. McKean has served on the editorial board of several statistical journals, including the Journal of the American Statistical Association, the Journal of Statistical Computation and Simulation, and the Journal of Nonparametric Statistics. Dr. McKean has published extensively on robust rank-based procedures for linear models. These include papers on the theory for robust estimation and testing, the geometry of robust procedures, and the small sample properties of robust inference. He has worked with general robust estimates, bounded inuence estimates, and high breakdown estimates. He has co-authored a series of papers on diagnostic procedures for robust estimation. Besides robust procedures, Dr. McKean has published in the areas of generalized linear models, nonparametric statistics and time series analyses. He has recently published articles on rank-based procedures for nonlinear, mixed, and GEE models. He is a co-author (with T.P. Hettmansperger) of the monograph Robust Nonparametric Statistical Methods. He has worked on algorithm development and software for these procedures including the R package Rfit and has co-authored (with J.D. Kloke) the book Nonparametric Statistical Methods Using R. His current investigations include rank-based algorithms for Big Data, rank-based Bayesian methods for linear and mixed models, visualization techniques, and robust methods for linear models with autoregressive errors. Dr. McKean has served as the dissertation advisor for twenty-six PhD students. He is a co-author, (with R.V. Hogg), of the text, Introduction to Mathematical Statistics.

Inhalt
1 Rank-Based Analysis of Linear Models and Beyond: A Review.- 2 Robust Signed-Rank Variable Selection in Linear Regression.- 3 Generalized Rank-Based Estimates for Linear Models with Cluster Correlated Data.- 4 Iterated Reweighted Rank-Based Estimates for GEE Models.- 5 On the Asymptotic Distribution of a Weighted Least Absolute Deviation Estimate for a Bifurcating Autoregressive Process.- 6 Applications of Robust Regression to Big Data Problems.- 7 Rank-Based Inference for Multivariate Data in Factorial Designs.- 8 Two-Sample Rank-Sum Test for Order Restricted Randomized Designs.- 9 On a Partially Sequential Ranked Set Sampling Paradigm.- 10 A New Scale-Invariant Nonparametric Test for Two-Sample Bivariate Location Problem with Application.- 11 Influence Functions and Efficiencies of k-Step Hettmansperger-Randles Estimators for Multivariate Location and Regression.- 12 New Nonparametric Tests for Comparing Multivariate Scales Using Data Depth.- 13 Multivariate Autoregressive Time Series Using Schweppe Weighted Wilcoxon Estimates.- 14 Median Stable Distributions.- 15 Confidence Intervals for Mean Difference between Two Delta-distributions.