## Non-Parametric Statistical Diagnosis: Problems and MethodsThis 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 |

445 | |

### Other editions - View all

Non-Parametric Statistical Diagnosis: Problems and Methods E. Brodsky,B.S. Darkhovsky Limited preview - 2000 |

Non-Parametric Statistical Diagnosis: Problems and Methods E. Brodsky,B.S. Darkhovsky No preview available - 2010 |

### Common terms and phrases

algorithm alpha band alpha rhythm analysis assume assumptions asymptotically optimal b-mixing Brownian bridge change-border change-point problem Chapter characteristics coefficients coincidence consider contamination continuous function CUSUM and GRSh CUSUM method defined denote density function diagnostic sequence distribution function EEG segmentation EEG signal electrodes exists exponential smoothing false alarm finite number finite-dimensional distributions formulate functions f Gaussian GRSh methods homogeneous independent random variables interval Lebesgue measure Lemma mathematical expectation maximum mean value minimax moving sample nonparametric normalized delay number of change-points observations obtain OOOOOOOOOOOOOOOO parameter tē piecewise probabilistic probability problems of statistical proof random field random process random sequence rate of convergence regression respect retrospective scheme space stationary statistical diagnosis structural Subsection synchrocomplexes taking into account threshold vector weakly converges Wiener process zero