Non-Parametric Statistical Diagnosis: Problems and Methods

Front Cover
Springer Science & Business Media, Mar 14, 2013 - Mathematics - 452 pages
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.
 

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Contents

of random variables
29
statistical diagnosis
57
State of the art review
83
Retrospective methods of statistical diagnosis
127
of the linear functional regression
151
for regression relationships
195
Sequential methods of statistical diagnosis
219
detection methods
247
Statistical diagnosis problems for random fields
299
problems for random fields
317
Application of the changepoint analysis
333
stationary structure of EEG
342
synchronization in multichannel EEG
362
between signals or signal components
380
Appendix Algorithms of statistical diagnosis
407
Author Index
445

early detection
283

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