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

Artur Bryk. "Smoothing dichotomy in randomized fixed-design regression with strongly dependent errors based on a moving average." Applicationes Mathematicae 41.1 (2014): 67-80. <http://eudml.org/doc/280047>.

@article{ArturBryk2014,
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.},
author = {Artur Bryk},
journal = {Applicationes Mathematicae},
keywords = {kernel estimators; linear process; long-range dependence; randomization; fixed-design regression; smoothing dichotomy},
language = {eng},
number = {1},
pages = {67-80},
title = {Smoothing dichotomy in randomized fixed-design regression with strongly dependent errors based on a moving average},
url = {http://eudml.org/doc/280047},
volume = {41},
year = {2014},
}

TY - JOUR
AU - Artur Bryk
TI - Smoothing dichotomy in randomized fixed-design regression with strongly dependent errors based on a moving average
JO - Applicationes Mathematicae
PY - 2014
VL - 41
IS - 1
SP - 67
EP - 80
AB - 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.
LA - eng
KW - kernel estimators; linear process; long-range dependence; randomization; fixed-design regression; smoothing dichotomy
UR - http://eudml.org/doc/280047
ER -