Statistical estimation of the significant arguments set of the binary vector-function with corrupted values

Let $\Theta$ be the set of significant arguments of the unknown binary vector-function with the random uniformly distributed arguments and corrupted values. Algorithm for constructing the estimate $\Theta^*$ of $\Theta$ based on statistical estimates of function spectrum is proposed. For some function classes (particularly, for vectorial bent-functions and bijective mappings) we get asymptotic bounds of the data size sufficient for the successful work of the algorithm, i.e. $\mathbf P\{\Theta^*=\Theta\}\to1$.