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
Date Written: June 2005
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: Suggested Citation