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.

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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

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Asymptotic Normality
  • Bioassay
  • California
  • Coefficients
  • Distribution Functions
  • Equations
  • Errors
  • Lethal Dosage
  • Military Research
  • Normal Distribution
  • Numbers
  • Probability
  • Random Variables
  • Statistics
  • United States

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Graph Algorithms and Convex Optimization.
  • Regression Analysis.