Randomized Fixed Design Regression under Long-Range-Dependent Errors

Abstract

We consider a fixed-design regression model with long-range-dependent errors and introduce an artificial randomization of grid points at which observations are taken in order to diminish the impact of strong dependence. The resulting estimator is shown to exhibit smoothing dichotomy with the variance in both cases, diminishing more quickly than in the fixed-design case.

Keywords:

• Convergence of moments
• Kernel estimator
• Linear process
• Long- and short-range dependence
• Randomization
• Random- and fixed-design regression
• Smoothing dichotomy

Mathematics Subject Classification:

• Primary 60F05
• Secondary 60G35