Convergence and robustness of the Robbins-Monro algorithm truncated at randomly varying bounds

Han-Fu Chen, Lei Guo and Ai-Jun Gao

Stochastic Processes and their Applications, 1987, vol. 27, 217-231

Abstract: 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

Keywords: stochastic; approximation; randomly; varying; truncation; robustness; to; noise; necessary; and; sufficient; condition; for; convergence (search for similar items in EconPapers)
Date: 1987
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Citations: View citations in EconPapers (5)

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