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Higher order representations of the Robbins-Monro process

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  • Dippon, Jürgen

Abstract

For quasi-linear regression functions, the Robbins-Monro process Xn is decomposed in a sum of a linear form and a quadratic form both defined in the observation errors. Under regularity conditions, the remainder term is of order O(n-3/2) with respect to the Lp-norm. If a cubic form is added, the remainder term can be improved up to an order of O(n-2). As a corollary the expectation of Xn is expanded up to an error of order O(n-2). This is used to correct the bias of Xn up to an error of order O(n-3/2 log n).

Suggested Citation

  • Dippon, Jürgen, 2004. "Higher order representations of the Robbins-Monro process," Journal of Multivariate Analysis, Elsevier, vol. 90(2), pages 301-326, August.
    • Handle: RePEc:eee:jmvana:v:90:y:2004:i:2:p:301-326
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