Chaudhuri , Probal
(1991)
*Nonparametric estimates of regression quantiles and their local Bahadur representation*
The Annals of Statistics, 19
(2).
pp. 760-777.
ISSN 0090-5364

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Official URL: http://projecteuclid.org/euclid.aos/1176348119

Related URL: http://dx.doi.org/10.1214/aos/1176348119

## Abstract

Let (X,Y) be a random vector such that X is d-dimensional, Y is real valued and Y=θ(X)+ε, where X and ε are independent and the αth quantile of ε is 0 (α is fixed such that 0<α<1). Assume that θ is a smooth function with order of smoothness p>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 a pointwise estimate Tˆn of T(θ), based on a set of i.i.d. observations (X_{1},Y_{1}),⋯,(S_{n},Y_{n}), that achieves the optimal nonparametric rate of convergence n^{−r} under appropriate regularity conditions. Further, a local Bahadur type representation is shown to hold for the estimate Tˆn and this is used to obtain some useful asymptotic results.

Item Type: | Article |
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Source: | Copyright of this article belongs to Institute of Mathematical Statistics. |

Keywords: | Regression Quantiles; Bahadur Representation; Optimal Nonparametric Rates Of Convergence |

ID Code: | 74614 |

Deposited On: | 25 Jun 2012 13:35 |

Last Modified: | 25 Jun 2012 13:35 |

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