Lio, Y. L.; Padgett, W. J. - In: Statistics & Probability Letters 11 (1991) 3, pp. 243-249
Let F(x) be a distribution function and let [xi]p denote the pth quantile for 0 < p < 1. In this note Nadaraya's estimator of [xi]p is considered. It is shown that the bandwidth h0 = C(k, f, K, p)n-1/(2k - 1) for k [greater-or-equal, slanted] 2 is asymptotically optimal in the sense that [p(n, h0) - [xi]p]2/infh[p(n, h) - [xi]p]2 --> 1 in probability as n -- [infinity], where p(n, h) denotes the estimator depending on the sample size n and the bandwidth h and C(k, f, K, p) is a constant depending on k, p, the density function f of F, and the...</p>