Non-Parametric Statistical Diagnosis: Problems and Methods

ISBN-13: 9780792363286 / Angielski / Twarda / 2000 / 452 str.

B. E. Brodsky; B. S. Darkhovsky; B. S. Darkhovsky

Opis

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.

Recenzje

`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

Spis treści

Preface. Part 1: Theory. 1. Preliminary considerations. 2. State of the art review. 3. Retrospective methods of statistical diagnosis for random sequences: change-point problems. 4. Retrospective methods of statistical diagnosis for random processes: `Contamination' problems. 5. Sequential methods of statistical diagnosis. 6. Statistical diagnosis problems for random fields. Part 2: Applications. 7. Application of the change-point analysis to investigation of the brain electrical activity. 8. Methods of statistical diagnosis in economic and financial systems. Appendix. Bibliography. Author Index. Subject Index. Main Notations and Abbreviations.