Global nonparametric estimation of conditional quantile functions and their derivatives

Chaudhuri, Probal (1991) Global nonparametric estimation of conditional quantile functions and their derivatives Journal of Multivariate Analysis, 39 (2). pp. 246-269. ISSN 0047-259X

Full text not available from this repository.

Official URL: http://linkinghub.elsevier.com/retrieve/pii/004725...

Related URL: http://dx.doi.org/10.1016/0047-259X(91)90100-G

Abstract

Let (X, Y) be a random vector such that X is d-dimensional, Y is real valued, and θ(X)is the conditional αth quantile ofY given X, where α is a fixed number such that 0 lt;α lt; 1. Assume that θ is a smooth function with order of smoothness p gt; 0, and set r=(p-m)/(2p+d), where m is a nonnegative integer smaller than p. Let T(θ) denote a derivative of θ of order m. It is proved that there exists estimate Tnof T(θ), based on a set of i.i.d. observations (X1, Y1), ..., (Xn, Yn), that achieves the optimal nonparametric rate of convergence n-r in Lq-norms (1≤q lt; ∞) restricted to compacts under appropriate regularity conditions. Further, it has been shown that there exists estimate Tn of T(θ) that achieves the optimal rate (n/log n)-r in L∞-norm restricted to compacts.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Regression Quantiles; Nonparametric Estimates; Bin Smoothers; Optimal Rates of Convergence
ID Code:8116
Deposited On:26 Oct 2010 04:31
Last Modified:26 Oct 2010 04:31

Repository Staff Only: item control page