Recursive estimation

A methodology for estimating parameters from data that arrive sequentially (and thus constitute a stochastic process, cf. also Sequential analysis). The motivation stems from real-time measurement systems in electrical engineering, and medical recording instruments. Whereas the arithmetic average and extreme values can be easily computed by updating mechanisms, the estimation of population quantiles (cf. Quantile) is a non-trivial problem. For this purpose, L. Tierney [a1] and U. Holst [a2] apply the stochastic approximation theory of H. Robbins and S. Monro [a3] (cf. also Stochastic approximation). Another approach uses quantiles of successive subsets [a4], in which case the asymptotic distribution is determined by recursive application of polynomials. A tree-based method with alternating minima and maxima is described in [a5].

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