Recursive estimation of quantitles using recursive kernel density estimators

Abstract

Recursive estimation of quantiles may be obained via adaptive stochastic approximation approximation theorms can be used to obtained the asympotic properties when the obervation are independent. for dependent sequences matingale theory cannot be applied straight forwardly as the tool for asympototic analysis.In this paper we consider both the case when the observation are i.i.d. and when they form a stationary and strongly regular process.the main result is sufficient condition for almost sure convergence in the strongly regular case.