Parametric and nonparametric inference from record-breaking data
This book presents a collection of methods for statistical inference based on record values in a sample. From the preface: \textit{B. C. Arnold}, \textit{N. Balakrishnan}, and \textit{H. N. Nagaraja} [Records. (1998; Zbl 0914.60007)] gave an excellent, comprehensive review of most of the results on records, including some material on inference from record-breaking data. However, their chapter on inference from such data is somewhat brief, discussing mainly the estimation of parameters and not the more general problem of parametric and nonparametric inference from record-breaking data. The main purpose of the present monograph is therefore to fill the inference gap mentioned above. Although inferences for parametric models are presented briefly, along with a summary of some of the results on prediction of future records, we focus on catalogueing the results on nonparametric inference from record-breaking data. Included is some material on parametric and nonparametric Bayesian models as well as a discussion of trend models. As a result, the material presented in this monograph provides a good supplement on inference from record-breaking data for a graduate course on the general topic of records. It should also serve as a valuable reference work on this topic for statisticians, probabilists, mathematicians, and other researchers. A description of the chapter headings is as follows: Chapter 1, Introduction. (pp. 1-4); Chapter 2, Preliminaries and early work. (pp. 5-9); Chapter 3, Parametric inference. (pp. 11-32); Chapter 4, Nonparametric inference -- genesis. (pp. 33-44); Chapter 5, Smooth function estimation. (pp. 45-65); Chapter 6, Bayesian models. (pp. 67-80); Chapter 7, Record models with trend. (pp. 81-104). The bibliography contains 81 items.
scientific article; zbMATH DE number 1879003