The Berry-Esseen inequality for the distribution of the least square estimate

A nonlinear regression modelx_t=g_t(₀)+ _t,t1, is considered. Under a number of conditions on its elements _t and gt(₀) it is proved that the distribution of the normalized least square estimate of the parameter ₀ converges uniformly on the real axis to the standard normal law at least as quickly as a quantity of the order T^–1/2 as T , where T is the size of the sample, by which the estimate is formed.Translated from Matematicheskie Zametki, Vol. 20, No. 2, pp. 293–303, August, 1976.