Accession Number:

ADA027395

Title:

A Stochastic Newton-Raphson Method.

Descriptive Note:

Technical rept.,

Corporate Author:

CASE WESTERN RESERVE UNIV CLEVELAND OHIO DEPT OF MATHEMATICS AND STATISTICS

Personal Author(s):

• Anbar,Dan

Report Date:

1976-07-01

Pagination or Media Count:

18.0

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 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.

Descriptors:

• *STOCHASTIC PROCESSES
• *APPROXIMATION(MATHEMATICS)
• LEAST SQUARES METHOD
• THEOREMS

Subject Categories:

• Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE