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

Tinbergen Institute Discussion Papers No. TI 2005-067/4

24 Pages Posted: 24 Jun 2005

See all articles by Yebin Cheng

Yebin Cheng

Tinbergen Institute - Tinbergen Institute Amsterdam (TIA); University of Amsterdam - Department of Quantitative Economics (KE)

Jan G. De Gooijer

University of Amsterdam - Department of Quantitative Economics (KE)

Date Written: June 2005

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 min a E(p (a,Y) | X = x), where the loss function p (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 and spot prices to compare its performance in practice with the "usual" squared-loss regression estimator.

Keywords: Asymptotic representation; Kernel function; Robust estimator; Strongly-mixing

JEL Classification: C14

Suggested Citation

Cheng, Yebin and De Gooijer, Jan G., Bahadur Representation for the Nonparametric M-Estimator Under Alpha-Mixing Dependence (June 2005). Tinbergen Institute Discussion Papers No. TI 2005-067/4. Available at SSRN: https://ssrn.com/abstract=748885 or http://dx.doi.org/10.2139/ssrn.748885

Yebin Cheng (Contact Author)

Tinbergen Institute - Tinbergen Institute Amsterdam (TIA) ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands
+31(0)20 525 7110 (Phone)

University of Amsterdam - Department of Quantitative Economics (KE) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

Jan G. De Gooijer

University of Amsterdam - Department of Quantitative Economics (KE) ( email )

Roetersstraat 11
Amsterdam, 1018 WB
Netherlands

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