Bahadur Representation for the Nonparametric M-Estimator Under Alpha-mixing Dependence

Yebin Cheng () and Jan G. Gooijer
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Yebin Cheng: Faculty of Economics and Econometrics, Universiteit van Amsterdam

No 05-067/4, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: Under the condition that the observations, which come from a high-dimensional population (X,Y), are strongly stationary and strongly-mixing, through using the local linear method, we investigate, in this paper, the strong Bahadur representation of the nonparametric M-estimator for the unknown function m(x)=arg minaIE(r(a,Y)|X=x), where the loss function r(a,y) is measurable. Furthermore, some related simulations are illustrated by using the cross validation method for both bivariate linear and bivariate nonlinear time series contaminated by heavy-tailed errors. The M-estimator is applied to a series of S&P 500 index futures andspot prices to compare its performance in practice with the "usual" squared-loss regression estimator.

Keywords: Asymptotic representation; Kernel function; Robust estimator; Strongly-mixing (search for similar items in EconPapers)
JEL-codes: C14 (search for similar items in EconPapers)
Date: 2005-06-21
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