G8 estimator of solutions of systems of linear algebraic equations

For linear forms of regularized solutions (x, c)=Re c' · ReI + i)+A'A_n ^–1]^–1 A'_nb of systems of equations Ax=b, where A is an n×m matrix, x, c, b are vectors, and _n is a sequence of constants, we propose the estimator , where is any measurable solution of the equation ()Re1+₁a(())]²+ (₁–₂)(1+₁(gq()))=, a(y)=n^–1 SpIy+^–1Z_s'Z^s+ iI]^–1, , _i=n_n ²_n ^–1s_n ^–1, ⁿ=mI_n ²_n ^–1s_n ^–1, X_i are independent observations on the matrix A. Under certain conditions, it is proved that G₈ is a consistent estimator for n and 0.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 66, pp. 111–119, 1988.