Statistical methods of search for coordinate set on which a random vector has bans

A stationary sequence of random vectors of length $L$ with the distribution of a random vector $\xi$ is observed. Coordinates of vectors in it take values in a finite set. The following hypothesis is considered: there is a set $\Theta\subset\{1,\dots,L\}$ such that the subvector $\xi_\Theta$ (being the projection of $\xi$ onto coordinates with numbers in $\Theta$) has the distribution of a given random vector $\eta$ with the distribution having bans. A concordance criterion is constructed by the analysis of an empirical distribution bans. In the case of the hypothesis validity (a priori), three algorithms to search for a part of $\Theta$ are proposed. They work under various portions of the information about the random vector $\eta$ distribution.