Abstract
Abstract A stochastic approximation procedure of the Robbins-Monro type is considered. The original idea behind the Newton-Raphson method is used as follows. Given n approximations X 1 ,…, X n with observations Y 1 ,…, Y n , a least squares line is fitted to the points ( X m , Y m ),…, ( X n , Y n ) where m n may depend on n . The ( n +1)st approximation is taken to be the intersection of the least squares line with y =0. A variation of the resulting process is studied. It is shown that this process yields a strongly consistent sequence of estimates which is asymptotically normal with minimal asymptotic variance.
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