Minimax filtration of linear transformations of stationary consequences - Moklyachuk , M. P. (Ukrains’kyi Matematychnyi Zhurnal, 1991)
We will consider the problem of determining a linear, mean-square optimal estimate of the transformation $Aξ = \sum_{j=0}^{∞}a(j)ξ(-j)$ of a stationary random sequence $ξ(k)$ with density $f (λ)$ from observations of the sequence $ξ(k)+η(k)$ with $k≤ 0$, where $η(k)$ is a stationary sequence not correlated with $ξ (k)$ with density $g(λ)$. The least favorable spectral densities $f_0(λ)\in D_f$, $g_0(λ)\in D_g$, and minimax (robust) spectral characteristics of an optimal estimate $Aξ$ for different classes of densities $D_f$, $D_g$.