SHARP CONVERGENCE-RATES OF STOCHASTIC-APPROXIMATION FOR DEGENERATE ROOTS

Sharp convergence rates of stochastic approximation algorighms are giv en for the case where the derivative of the unknown regression functio n at the sought-for root is zero. The convergence rates obtained are s harp for the general step size used in the algorithms in contrast to t he previous work where they are not sharp for slowly decreasing step s izes; all possible limit points are found for the case where the first matrix coefficient in the expansion of the regression function is nor mal; and the estimation upper bound is shown to be achieved for the mu lti-dimensional case in contrast to the previous work where only the o ne-dimensional result is proved.