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

### Volume 41 / 2014

Applicationes Mathematicae 41 (2014), 67-80
MSC: 62G08, 62G20, 62M10.
DOI: 10.4064/am41-1-6

#### Abstract

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.