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Two Approximations to the Robbins Monro Process
UNIVERSITY OF CALIFORNIA Oakland United States
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The following process was introduced by Robbins and Monro 1. For each real number x let Yx be a random variable such that EYx Mx exists. We assume that M is Borel measurable, that the regression equation Mx a has a single root theta, which we wish to estimate, and that x - theta Mx - a 0 for all x does not equal theta. An initial value xi and a sequence asub n. of positive numbers are selected. The n 1 approximation to theta is defined inductively by the formula.
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