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

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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 T_{n}of T(θ), based on a set of i.i.d. observations (X_{1}, Y_{1}), ..., (X_{n}, Y_{n}), that achieves the optimal nonparametric rate of convergence n^{-r} in L_{q}-norms (1≤q lt; ∞) restricted to compacts under appropriate regularity conditions. Further, it has been shown that there exists estimate T_{n} of T(θ) that achieves the optimal rate (n/log n)^{-r} in L∞-norm restricted to compacts.

Item Type: | Article |
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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 |

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