A new theoretical and algorithmical basis for estimation, identification and control.

*(English)*Zbl 0608.93002A new theory applicable to data treatment is briefly exposed. This (gnostical) theory derives a mathematical model of data disturbed by uncertainly, the statistical model of which may be unknown or even unjustifiable. Gnostical theory is based on two simple axioms. It results in laws governing the uncertainty of each individual datum such as variational principles of virtual kinematics of real data and of their dynamics, closely related to entropy and information of data. Algorithms resulting from gnostical theory maximize the information obtained from data and yield data characteristics robust with respect to outlying or inlying data. Fields of application include the estimation of both location and scale parameters of small data samples and of their generalized correlations, robust estimation of probability and of probability distribution, non-linear discrete filtering, prediction and smoothing, identification of systems strong disturbances and adaptive setting of alarm systems, robust identification of regression models, robust control, cluster analysis etc.

Reviewer: J.Just

##### MSC:

93A05 | Axiomatic systems theory |

68U20 | Simulation (MSC2010) |

93E10 | Estimation and detection in stochastic control theory |

62H30 | Classification and discrimination; cluster analysis (statistical aspects) |

93B30 | System identification |

93B35 | Sensitivity (robustness) |

93C40 | Adaptive control/observation systems |

93E11 | Filtering in stochastic control theory |

93E12 | Identification in stochastic control theory |

62M20 | Inference from stochastic processes and prediction |

94A15 | Information theory (general) |

93E14 | Data smoothing in stochastic control theory |

93E25 | Computational methods in stochastic control (MSC2010) |

##### Keywords:

cognitive systems; Gnostical theory; uncertainty; robust estimation; non- linear discrete filtering; robust control
Full Text:
DOI

##### References:

[1] | Jumarie, G.A., A relativistic information theory model for general systems, Int. J. syst. sci., 6, 865-886, (1975) · Zbl 0311.94015 |

[2] | Jumarie, G.A., Subjectivity, information, systems. introduction to a theory of relativistic cybernetics, (1985), Gordon and Breach New York |

[3] | Kovanic, P., Gnostical theory of individual data, Probl. control inf. theory, 13, 259-274, (1984) · Zbl 0575.94005 |

[4] | Kovanic, P., Gnostical theory of small samples of real data, Probl. control inf. theory, 303-319, (1984) · Zbl 0583.94008 |

[5] | Kovanic, P., On relations between information and physics, Probl. control inf. theory, 13, 383-399, (1984) · Zbl 0565.94009 |

[6] | Kovanic, P. and J. Novovičová (1986). (to appear). |

[7] | Krants, D.H.; Luce, R.D.; Suppes, P.; Tversky, A., Foundations of measurement, (1971), Academic Press New York |

[8] | Stigler, S.M., Do robust estimators work with real data?, Ann. statist., 5, 1055-1098, (1977) · Zbl 0374.62050 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.