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A Stochastic Newton-Raphson Method.
CASE WESTERN RESERVE UNIV CLEVELAND OHIO DEPT OF MATHEMATICS AND STATISTICS
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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 observation Y1,...,Yn, a least squares line is fitted to the points Xm,Ym,...,Xn,Yn where m n may depend on n. The n1st 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.
APPROVED FOR PUBLIC RELEASE