Minimax extrapolation of random processes for models of \(\varepsilon\)- pollution. (English. Russian original) Zbl 0748.62051

Moklyachuk, M. P.

Theory Probab. Math. Stat. 42, 113-121 (1991); translation from Teor. Veroyatn. Mat. Stat., Kiev 42, 95-103 (1990).

Summary: The problem of linear estimation is considered for the transform \[ A\xi=\sum^ \infty_{j=0}a(j)\xi(j) \] of a stationary random process \(\xi(j)\) with density \(f(\lambda)\) from observations of \(\xi(j)\) of \(j<0\). Least favorable spectral densities \(f_ 0(\lambda)\in {\mathcal D}\) and minimax (robust) spectral characteristics of an optimal estimator of \(A\xi\) are found for different classes \(\mathcal D\) of densities.

MSC:

62M15	Inference from stochastic processes and spectral analysis
62M20	Inference from stochastic processes and prediction

Keywords:

minimax extrapolation; models of epsilon-pollution; minimax robust spectral characteristics; linear estimation; stationary random process; least favorable spectral densities; optimal estimator