Two Approximations to the Robbins Monro Process
Abstract
The following process was introduced by Robbins and Monro [1]. For each real number x let Y(x) be a random variable such that E[Y(x)] = M(x) exists. We assume that M is Borel measurable, that the regression equation M(x) = a has a single root theta, which we wish to estimate, and that (x - theta) [M(x) - a] > 0 for all x does not equal theta. An initial value xi and a sequence {a(sub n).} of positive numbers are selected. The (n + 1) approximation to theta is defined inductively by the formula.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1956
- Accession Number
- AD1028383
Entities
People
- E. L. Lehmann
- J Jr L Hodges
Organizations
- University of California