Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/56880
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Type: Journal article
Title: Local linear spatial quantile regression
Author: Hallin, M.
Lu, Z.
Yu, K.
Citation: Bernoulli: a journal of mathematical statistics and probability, 2009; 15(3):659-686
Publisher: Int Statistical Inst
Issue Date: 2009
ISSN: 1350-7265
Statement of
Responsibility: 
Marc Hallin, Zudi Lu, and Keming Yu
Abstract: Let {(Y i, X i), i ∈ ℤ n} be a stationary real-valued (d + 1)-dimensional spatial processes. Denote by x → qp(x). P ∈ (0,1), x ∈ ℝ d, the spatial quantile regression function of order p, characterized by P{Y i[≤ qp(x)|X i=x} = p. Assume that the process has been observed over an N-dimensional rectangular domain of the form I n : = {i = (i 1...,i N) ∈ ℤ N|1 ≤ k ≤n k, k= l,...,N}, with n = (n 1.....n N) ∈ℤ N. We propose a local linear estimator of q p. That estimator extends to random fields with unspecified and possibly highly complex spatial dependence structure, the quantile regression methods considered in the context of independent samples or time series. Under mild regularity assumptions, we obtain a Bahadur representation for the estimators of q p and its first-order derivatives, from which we establish consistency and asymptotic normality. The spatial process is assumed to satisfy general mixing conditions, generalizing classical time series mixing concepts. The size of the rectangular domain I n is allowed to tend to infinity at different rates depending on the direction in ℤ N (non-isotropic asymptotics). The method provides much richer information than the mean regression approach considered in most spatial modelling techniques. © 2009 ISI/BS.
Keywords: Bahadur representation
local linear estimation
random fields
quantile regression
DOI: 10.3150/08-BEJ168
Description (link): http://projecteuclid.org/euclid.bj/1251463276
Published version: http://dx.doi.org/10.3150/08-bej168
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