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Title: Local linear spatial quantile regression
Authors: Hallin, M
Lu, Z
Yu, K
Keywords: Bahadur representation;Local linear estimation;Random fields;Quantile regression
Issue Date: 2009
Publisher: Bernoulli Society for Mathematical Statistics and Probability
Citation: Bernoulli, 15(3), 659 - 686, 2009
Abstract: Let {(Yi,Xi), i ∈ ZN} be a stationary real-valued (d + 1)-dimensional spatial processes. Denote by x → qp(x), p ∈ (0, 1), x ∈ Rd , the spatial quantile regression function of order p, characterized by P{Yi ≤ qp(x)|Xi = x} = p. Assume that the process has been observed over an N-dimensional rectangular domain of the form In := {i = (i1, . . . , iN) ∈ ZN|1 ≤ ik ≤ nk, k = 1, . . . , N}, with n = (n1, . . . , nN) ∈ ZN. We propose a local linear estimator of qp. 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 qp 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 In is allowed to tend to infinity at different rates depending on the direction in ZN (non-isotropic asymptotics). The method provides much
Description: Copyright @ 2009 International Statistical Institute / Bernoulli Society for Mathematical Statistics and Probability.
ISSN: 1350-7265
Appears in Collections:Publications
Dept of Mathematics Research Papers
Mathematical Sciences

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