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A stochastic Newton-Raphson method
Authors:Dan Anbar
Institution:Case Western Reserve University, Israel;Tele Aviv University, Israel
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 X1,…, Xn with observations Y1,…, Yn, a least squares line is fitted to the points (Xm, Ym),…, (Xn, Yn) 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.
Keywords:62L20  62L05  Stochastic Approximation  Robbins-Monro Procedure  Efficient Estimation
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