Non-Parametric Statistical Diagnosis: Problems and Methods: 509 (Mathematics and Its Applications, 509) - Hardcover

Brodsky, E.; Darkhovsky, B.S.

Hardcover

ISBN 10: 0792363280 ISBN 13: 9780792363286

Publisher: Springer, 2000

Synopsis

This book has a distinct philosophy and it is appropriate to make it explicit at the outset. In our view almost all classic statistical inference is based upon the assumption (explicit or implicit) that there exists a fixed probabilistic mechanism of data generation. Unlike classic statistical inference, this book is devoted to the statistical analysis of data about complex objects with more than one probabilistic mechanism of data generation. We think that the exis­ tence of more than one data generation process (DGP) is the most important characteristic of com plex systems. When the hypothesis of statistical homogeneity holds true, Le., there exists only one mechanism of data generation, all statistical inference is based upon the fundamentallaws of large numbers. However, the situation is completely different when the probabilistic law of data generation can change (in time or in the phase space). In this case all data obtained must be 'sorted' in subsamples generated by different probabilistic mechanisms. Only after such classification we can make correct inferences about all DGPs. There exists yet another type of problem for complex systems. Here it is important to detect possible (but unpredictable) changes of DGPs on-line with data collection. Since the complex system can change the probabilistic mechanism of data generation, the correct statistical analysis of such data must begin with decisions about possible changes in DGPs.

About this title

Review

`Overall, the book is nicely organized, and the material is clearly presented. The book has several strengths. I found Non-Parametric Statistical Diagnosis to be an interesting book to add to the area of change-point analysis.'
Journal of the American Statistical Association, September 2001

Synopsis

This volume gives a systematic account of various problems of statistical diagnostics - the detection of changes in probabilistic characteristics of random processes and fields. Methods of solving such problems are proposed, based upon a unified non-parametric approach. Two general formalizations of the problems of statistical diagnostics are considered: firstly, the detection of changes in arbitrary probabilistic distributions of random processes and fields, "glued" from different stationary pieces - in other words, the detection of moments or areas of such "glueing"; and secondly, the detection of statistical "contamination" in data (realizations of random fields or processes), or "abnormal" observations with deviating statistical characteristics. A general approach to solving such problems is proposed, which is based upon the principle of reduction to certain standard situations and which does not use a priori data about probabilistic distributions. Much attention is paid to applications in such diverse areas as biology (EECs) and economics.

The book should be of interest to researchers in statistics and random processes, as well as advanced undergraduate and postgraduate students in the same disciplines, and to specialists in control theory, systems analysis, biomedical engineering, and econometrics.

Edition details

• Publisher: Springer
• Publication date: 2000
• Language: English
• ISBN 10: 0792363280
• ISBN 13: 9780792363286
• Binding: Hardcover
• Number of pages: 467