an:02177056
Zbl 1117.62489
Dobrovidov, A. V.
Convergence rates of nonparametric filtering estimates in autoregression dynamic systems
EN
Autom. Remote Control 64, No. 1, 49-64 (2003); translation from Avtom. Telemekh. 2003, No. 1, 56-73 (2003).
00108511
2003
j
62M20 62G05 94A12 62M10
Summary: The Bayes problem of filtration of a random process from observations on an autoregression process with coefficients defined by functions of the useful signal is studied. The main assumption asserts that the conditional observation densities belong to a family of conditional exponential densities with known functions of observations and useful signal, whose distribution is not known in advance. Optimal signal filtering equations and empirical risk estimates are derived. Regularized nonparametric filtering estimates are derived and a theorem on the mean-square convergence and convergence rates of these estimates is formulated.