A new stochastic approximation procedure using quantile curves

Summary Suppose that for each real number x we can sample at will from a population having unknown distribution function F _x (·), that p is a fixed number in (0,1), that a is a fixed real number, and that there is a unique unknown value of x (call it ) such that is the p-th quantile of F .We propose scheme for sequentially approximating , present a theorem giving conditions under which these approximations converge to with probability one, discuss the conditions of the theorem, give some examples, and mention some variations.The research of this author was supported by National Science Foundation Grant No. MCS 77-00841The research of this author was supported by the Research Foundation of the State University of New York