Minimax filtration of linear transformations of stationary sequences
A linear least squares estimation problem is considered for the transformation \(A\xi =\sum^{\infty}_{j=0}a(j)\xi (-j)\) of a stationary stochastic sequence \(\xi\) (j) with spectral density f(\(\lambda\)) using observations of \(\xi (j)+\eta (j)\), \(j\leq 0\), where \(\eta\) (j) is a stationary sequence with spectral density g(\(\lambda\)). Least favourable spectral densities \(f_ 0(\lambda)\in {\mathcal D}_ f\), \(g_ 0(\lambda)\in {\mathcal D}_ g\), and minimax (robust) spectral characteristics of the optimal estimator of \(A\xi\) are found for different classes of spectral densities.
linear transformations of stationary sequences
scientific article; zbMATH DE number 4201435