### Abstract

The mean square upper bound of the difference between the error probability of Bayesian decision and the decision error probability connected with some estimates of Bayesian decision function is known for two hypotheses testing problems. The convergence of the mean square minimization algorithm is also proved for weakly dependent labeled samples. This paper presents an improved upper bound given by the mean distances of Bayesian decision functions and their estimates for multihypotheses testing. A slight modification of this upper bound might actually be minimized over the space of given finite dimensional decision functions. It is an adaptive recursive algorithm, a version of stochastic approximation particularly suited to certain tasks in statistical pattern recognition and related control problems.

Original language | English |
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Pages (from-to) | 449-457 |

Number of pages | 9 |

Journal | Probl Control Inf Theory |

Volume | 5 |

Issue number | 5-6 |

Publication status | Published - jan. 1 1976 |

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### ASJC Scopus subject areas

- Engineering(all)