Parametric and Nonparametric Inference from Record-Breaking Data

by Gulati, Sneh; Padgett, William J.

• ISBN13: 9780387001388
• ISBN10: 0387001387
• Format: Paperback
• Copyright: 2003-01-01
• Publisher: Springer Nature

Summary

This book provides a comprehensive look at statistical inference from record-breaking data in both parametric and nonparametric settings, including Bayesian inference. A unique feature is that it treats the area of nonparametric function estimation from such data in detail, gathering results on this topic to date in one accessible volume. Previous books on records have focused mainly on the probabilistic behavior of records, prediction of future records, and characterizations of the distributions of record values, addressing some inference methods only briefly. The main purpose of this book is to fill this void on general inference from record values.Statisticians, mathematicians, and engineers will find the book useful as a research reference and in learning about making inferences from record-breaking data. The book can also serve as part of a graduate-level statistics or mathematics course, complementing material on the probabilistic aspects of record values. For a basic understanding of the statistical concepts, a one-year graduate course in mathematical statistics provides sufficient background. For a detailed understanding of the convergence theory of the nonparametric function estimators, a course in measure theory or probability theory at the graduate level is useful. Sneh Gulati is Associate Professor of Statistics at Florida International University in Miami. She is currently an associate editor of the Journal of Statistical Computation and Simulation and has published several articles in statistics. Currently she serves as the president of the South Florida Chapter of the American Statistical Association and is also the chair of the Florida Commission of Hurricane Loss Projection Methodology.William J. Padgett is Professor of Statistics and was the founding Chair of the Department of Statistics at the University of South Carolina, Columbia. He has published numerous papers and articles, as well as three books, on statistics and probability and has served as an associate editor of eight statistical journals, including Technometrics, Lifetime Data Analysis, Naval Research Logistics, Journal of Statistical Computation and Simulation, and the Journal of Statistical Planning and Inference. He is a Fellow of both the American Statistical Association and the Institute of Mathematical Statistics and an elected ordinary member of the International Statistical Institute.

Table of Contents

Preface	v
Introduction	1	(4)
Preliminaries and Early Work	5	(6)
Notation and Terminology	6	(1)
Stochastic Behavior	7	(4)
Parametric Inference	11	(22)
General Overview	11	(1)
Parametric Inference Due to Samaniego and Whitaker	12	(5)
Exponential Distribution---Inverse Sampling	12	(2)
Exponential Distribution---Random Sampling	14	(3)
Parametric Inference Beyond Samaniego and Whitaker	17	(7)
The Problem of Prediction	24	(9)
Best Linear Unbiased Prediction	25	(3)
Best Linear Invariant Prediction	28	(1)
``Other'' Optimal Predictors	29	(1)
Prediction Intervals	30	(3)
Nonparametric Inference---Genesis	33	(12)
Introduction	33	(1)
The Work of Foster and Stuart	33	(3)
Nonparametric Maximum Likelihood Estimation	36	(3)
Asymptotic Results	39	(6)
Smooth Function Estimation	45	(22)
The Smooth Function Estimators---Definitions and Notation	46	(3)
Asymptotic Properties of the Smooth Estimators	49	(18)
Bayesian Models	67	(14)
Bayesian Prediction Intervals	67	(2)
One-Parameter Exponential Model	68	(1)
Two-Parameter Exponential Model	68	(1)
Laplace Approximations for Prediction	69	(4)
Bayesian Inference for the Survival Curve	73	(8)
Record Models with Trend	81	(24)
Introduction	81	(1)
The Models for Records with Trend	82	(2)
The Fα Model	82	(1)
The Pfeifer Model	83	(1)
The Linear Drift Model	84	(1)
The Geometric and the Pfeifer Models	84	(5)
The Geometric Model	84	(3)
The Pfeifer Model	87	(2)
Properties of the Linear Drift and Related Models	89	(11)
Early Work	89	(6)
Trend Models---The Work of Smith (1988) and Other Developments	95	(5)
The ``General Record Model''	100	(5)
References	105	(6)
Index	111