Smoothing dichotomy in randomized fixed-design regression with strongly dependent errors based on a moving average

Artur Bryk¹

¹ Department of Mathematics and Mathematical Economics Warsaw School of Economics Al. Niepodległości 162 02-554 Warszawa, Poland

Applicationes Mathematicae, Tome 41 (2014) no. 1, pp. 67-80.

Résumé

We consider a fixed-design regression model with errors which form a Borel measurable function of a long-range dependent moving average process. We introduce an artificial randomization of grid points at which observations are taken in order to diminish the impact of strong dependence. We show that the Priestley–Chao kernel estimator of the regression fuction exhibits a dichotomous asymptotic behaviour depending on the amount of smoothing employed. Moreover, the resulting estimator is shown to exhibit weak consistency (i.e. in probability). Simulation results indicate significant improvement when randomization is employed.

Détail

DOI : 10.4064/am41-1-6

Keywords: consider fixed design regression model errors which form borel measurable function long range dependent moving average process introduce artificial randomization grid points which observations taken order diminish impact strong dependence priestley chao kernel estimator regression fuction exhibits dichotomous asymptotic behaviour depending amount smoothing employed moreover resulting estimator shown exhibit weak consistency probability simulation results indicate significant improvement randomization employed