Local convergence theorems for adaptive stochastic approximation schemes.
For the regression model y = M(x) + epsilon, adaptive stochastic approximation schemes of the form x(n+1) = x(n) - y(n)/(nb(n)) for choosing the levels x(1),x(2),... at which y(1),y(2),... are observed converge with probability 1 to the unknown root theta of the regression function M(x). Certain local convergence theorems that relate the convergence rate of x(n) - theta to the limiting behavior of the random variables b(n) are established.
Lai
T L
TL
Department of Mathematical Statistics, Columbia University, New York, New York 10027.
Robbins
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