Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds
In this paper the Robbins-Monro (RM) algorithm with step-size an = 1/n and truncated at randomly varying bounds is considered under mild conditions imposed on the regression function. It is proved that for its a.s. convergence to the zero of a regression function the necessary and sufficient condition is where [xi]i denotes the measurement error. It is also shown that the algorithm is robust with respect to the measurement error in the sense that the estimation error for the sought-for zero is bounded by a function g([var epsilon]) such that
Volume (Year): 27 (1987)
Issue (Month): ()
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