Robust nonparametric regression in time series
Consider a stationary time series (Xt, Yt), t = 0, ±1, ... with Xt being d-valued and Yt real-valued. Let [psi](·) denote a monotone function and let [theta](·) denote the robust conditional location functional so that E[[psi](Y0 - [theta](X0))X0] = 0. Given a finite realization (X1, Y1), ..., (Xn, Yn), the problem of estimating [theta](·) is considered. Under appropriate regularity conditions, it is shown that a sequence of the robust conditional location functional estimators can be chosen to achieve the optimal rate of convergence n-1/(2 + d) both pointwise and in Lq (1 <= q < [infinity]) norms restricted to a compact; it can also be chosen to achieve the optimal rate of convergence (n-1 log(n))1/(2 + d) in L[infinity] norm restricted to a compact.
Year of publication: |
1992
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Authors: | Truong, Young K. |
Published in: |
Journal of Multivariate Analysis. - Elsevier, ISSN 0047-259X. - Vol. 41.1992, 2, p. 163-177
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Publisher: |
Elsevier |
Keywords: | kernel estimator local M-estimator nonparametric regression optimal rates of convergence stationary time series mixing processes |
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