Abstract
For the multidimensional stochastic systems obeying the regression models with unknown covariances of disturbances, consideration was given to the choice of a covariance model and estimation of its parameters. The invariant behavior of the regression model with the covariance matrix of a special structure was studied. In the problem of identifying the structure of a set of feasible covariance matrices, a procedure of successive testing of hypotheses was proposed. The unbiased and invariant uniformly optimal estimates of the parameters of the observation-based model were determined. The problem of identifying the model of covariances in experiment design with random factors was considered as an example.
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Translated from Avtomatika i Telemekhanika, No. 3, 2005, pp. 48–64.
Original Russian Text Copyright © 2005 by Sysoev, Shaikin.
This paper was recommended for publication by V.A. Lototskii, a member of the Editorial Board
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Sysoev, L.P., Shaikin, M.E. Identification of commutative covariance structures by successive testing of statistical hypotheses. Autom Remote Control 66, 382–397 (2005). https://doi.org/10.1007/s10513-005-0068-3
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DOI: https://doi.org/10.1007/s10513-005-0068-3