View source for Recursive estimation

A methodology for estimating parameters from data that arrive sequentially (and thus constitute a [[Stochastic process|stochastic process]], cf. also [[Sequential analysis|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|Quantile]]) is a non-trivial problem. For this purpose, L. Tierney [[#References|[a1]]] and U. Holst [[#References|[a2]]] apply the stochastic approximation theory of H. Robbins and S. Monro [[#References|[a3]]] (cf. also [[Stochastic approximation|Stochastic approximation]]). Another approach uses quantiles of successive subsets [[#References|[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 [[#References|[a5]]].

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  L. Tierney,   "A space-efficient recursive procedure for estimating a quantile of an unknown distribution"  ''SIAM J. Scient. Statist. Comp.'' , '''4'''  (1983)  pp. 706–711</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  U. Holst,   "Recursive estimation of quantiles using kernel density estimators"  ''Sequential Anal.'' , '''6'''  (1987)  pp. 219–237</TD></TR><TR><TD valign="top">[a3]</TD> <TD valign="top">  H. Robbins,   S. Monro,   "A stochastic approximation method"  ''Ann. Math. Stat.'' , '''22'''  (1951)  pp. 400–427</TD></TR><TR><TD valign="top">[a4]</TD> <TD valign="top">  P.J. Rousseeuw,   G.W. Bassett,   "The remedian: a robust averaging method for large data sets"  ''J. Amer. Statist. Assoc.'' , '''85'''  (1990)  pp. 97–104</TD></TR><TR><TD valign="top">[a5]</TD> <TD valign="top">  J. Pearl,   "A space-efficient on-line method of computing quantile estimators"  ''J. Algorithms'' , '''2'''  (1981)  pp. 164–177</TD></TR></table>