Error estimation for multidimensional analogue of the polygon of frequencies method

Decomposition to three components for $L_2$-error of multi-dimensional analogue of the polygon of frequencies method is obtained. For every component an upper bound is constructed. The statement about the finiteness of maximum of variances of stochastic estimates in grid nodes is derived. Upper bounds for displacements of estimates in nodes for $C$-approach and $L_2$-approach are obtained. On that basis it is shown that the application of smooth approximations of the solution for the polygon of frequencies method is inexpedient.