Parametric and Nonparametric Inference from Record-Breaking Data

ISBN-13: 9780387001388 / Angielski / Miękka / 2003 / 117 str.

Sneh Gulati; James J. Dugundji; W. J. Padgett

Opis

As statisticians, we are constantly trying to make inferences about the underlying population from which data are observed. This includes estimation and prediction about the underlying population parameters from both complete and incomplete data. Recently, methodology for estimation and prediction from incomplete data has been found useful for what is known as "record-breaking data," that is, data generated from setting new records. There has long been a keen interest in observing all kinds of records-in particular, sports records, financial records, flood records, and daily temperature records, to mention a few. The well-known Guinness Book of World Records is full of this kind of record information. As usual, beyond the general interest in knowing the last or current record value, the statistical problem of prediction of the next record based on past records has also been an important area of record research. Probabilistic and statistical models to describe behavior and make predictions from record-breaking data have been developed only within the last fifty or so years, with a relatively large amount of literature appearing on the subject in the last couple of decades. This book, written from a statistician's perspective, is not a compilation of "records," rather, it deals with the statistical issues of inference from a type of incomplete data, record-breaking data, observed as successive record values (maxima or minima) arising from a phenomenon or situation under study. Prediction is just one aspect of statistical inference based on observed record values.

Recenzje

 New record values in sports, finances, climate, ... are of interest to most people, and for about half a century, probabilists and statisticians have taken up the challenge of modelling their behaviour. The present monograph provides results on statistical inference problems for record-breaking data. For example: how to fit a parametric or nonparametric model to such data? Or also: how to predict the next record, based on the values of the past records. The main body of the book (Chapters 4-7) is a discussion of all the known work on nonparametric inference for this type of data.

The book will be a useful reference for researchers in this area. There could also be interest from engineers working in destructive stress testing and quality control.

ISI Short Book Reviews, Vol. 23/2, August 2003

Spis treści

1. Introduction.- 2. Preliminaries and Early Work.- 3. Parametric Inference.- 4. Nonparametric Inference—Genesis.- 5. Smooth Function Estimation.- 6. Bayesian Models.- 7. Record Models with Trend.- References.