Ebook: Nonparametric Methods in Change-Point Problems

The explosive development of information science and technology puts in new problems involving statistical data analysis. These problems result from higher re­ quirements concerning the reliability of statistical decisions, the accuracy of math­ ematical models and the quality of control in complex systems. A new aspect of statistical analysis has emerged, closely connected with one of the basic questions of cynergetics: how to "compress" large volumes of experimental data in order to extract the most valuable information from data observed. De­ tection of large "homogeneous" segments of data enables one to identify "hidden" regularities in an object's behavior, to create mathematical models for each seg­ ment of homogeneity, to choose an appropriate control, etc. Statistical methods dealing with the detection of changes in the characteristics of random processes can be of great use in all these problems. These methods have accompanied the rapid growth in data beginning from the middle of our century. According to a tradition of more than thirty years, we call this sphere of statistical analysis the "theory of change-point detection. " During the last fifteen years, we have witnessed many exciting developments in the theory of change-point detection. New promising directions of research have emerged, and traditional trends have flourished anew. Despite this, most of the results are widely scattered in the literature and few monographs exist. A real need has arisen for up-to-date books which present an account of important current research trends, one of which is the theory of non parametric change--point detection.

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This volume deals with nonparametric methods of change point (disorder) detection in random processes and fields. A systematic account is given of up-to-date developments in this rapidly evolving branch of statistics. It also provides a new approach to change point detection which is characterized by the reduction of change point problems to the more basic problem of mean value change points, and also the implementation of nonparametric statistics which require no a priori information concerning distributions.The book has seven chapters: Chapter 1 presents an account of preliminary considerations. Chapter 2 reviews the current state-of-the-art. Chapters 3 and 4 - the major chapters of the book - consider a posteriori change point problems and sequential change point detection problems, respectively. Chapter 5 discusses disorder detection of random fields, and Chapter 6 deals with applications in such diverse areas as geophysics, control systems and the analysis of historical texts. The volume concludes with a chapter devoted to new results, proofs and some technical details including an overview of a computer program package which has been developed for a posteriori change point detection.For researchers in the statistics and probability of random processes, this volume will also be of interest to specialists in control theory, engineering, systems analysis and cybernetics.