Variance function estimation via model selection

Teresa Ledwina, and Jan Mielniczuk. "Variance function estimation via model selection." Applicationes Mathematicae 37.4 (2010): 387-411. <http://eudml.org/doc/279956>.

@article{TeresaLedwina2010,
abstract = {The problem of estimating an unknown variance function in a random design Gaussian heteroscedastic regression model is considered. Both the regression function and the logarithm of the variance function are modelled by piecewise polynomials. A finite collection of such parametric models based on a family of partitions of support of an explanatory variable is studied. Penalized model selection criteria as well as post-model-selection estimates are introduced based on Maximum Likelihood (ML) and Restricted Maximum Likelihood (REML) methods of estimation of the parameters of the models. The estimators are defined as ML or REML estimators in the models with dimensions determined by respective selection rules. Some encouraging simulation results are presented and consistency results on the solution pertaining to ML estimation for this approach are proved.},
author = {Teresa Ledwina, Jan Mielniczuk},
journal = {Applicationes Mathematicae},
language = {eng},
number = {4},
pages = {387-411},
title = {Variance function estimation via model selection},
url = {http://eudml.org/doc/279956},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Teresa Ledwina
AU - Jan Mielniczuk
TI - Variance function estimation via model selection
JO - Applicationes Mathematicae
PY - 2010
VL - 37
IS - 4
SP - 387
EP - 411
AB - The problem of estimating an unknown variance function in a random design Gaussian heteroscedastic regression model is considered. Both the regression function and the logarithm of the variance function are modelled by piecewise polynomials. A finite collection of such parametric models based on a family of partitions of support of an explanatory variable is studied. Penalized model selection criteria as well as post-model-selection estimates are introduced based on Maximum Likelihood (ML) and Restricted Maximum Likelihood (REML) methods of estimation of the parameters of the models. The estimators are defined as ML or REML estimators in the models with dimensions determined by respective selection rules. Some encouraging simulation results are presented and consistency results on the solution pertaining to ML estimation for this approach are proved.
LA - eng
UR - http://eudml.org/doc/279956
ER -