Sequential statistical decision making in problems of data flows analysis

Abstract

In the problems of data flows analysis, the problems of statistical decision making on parameters of observed data flows are important. For their solution it is proposed to use sequential statistical decision rules. The rules are constructed for three models of observation flows: sequence of independent homogeneous observations; sequence of observations forming a time series with a trend; sequence of dependent observations forming a homogeneous Markov chain. For each case the situation is considered, where the model describes the observed stochastic data with a distortion. "Outliers" ("contamination") are used as the admissible distortions that adequately describe the majority of situations appear in practice. For such situations the families of sequential decision rules are proposed, and robust decision rules are constructed that allow to reduce influence of distortion to the efficiency characteristics. The results of computer experiments are given to illustrate the constructed decision rules.