TY - JOUR
T1 - Variance function additive partial linear models
AU - Fang, Yixin
AU - Lian, Heng
AU - Liang, Hua
AU - Ruppert, David
PY - 2015/8/19
Y1 - 2015/8/19
N2 - To model heteroscedasticity in a broad class of additive partial linear models, we allow the variance function to be an additive partial linear model as well and the parameters in the variance function to be different from those in the mean function. We develop a two-step estimation procedure, where in the first step initial estimates of the parameters in both the mean and variance functions are obtained and then in the second step the estimates are updated using the weights based on the initial estimates. We use polynomial splines to approximate the additive nonparametric components in both the mean and variation functions and derive their convergence rates. The resulting weighted estimators of the linear coefficients in both the mean and variance functions are shown to be asymptotically normal and more efficient than the initial un-weighted estimators. Simulation experiments are conducted to examine the numerical performance of the proposed procedure, which is also applied to analyze the dataset from a nutritional epidemiology study.
AB - To model heteroscedasticity in a broad class of additive partial linear models, we allow the variance function to be an additive partial linear model as well and the parameters in the variance function to be different from those in the mean function. We develop a two-step estimation procedure, where in the first step initial estimates of the parameters in both the mean and variance functions are obtained and then in the second step the estimates are updated using the weights based on the initial estimates. We use polynomial splines to approximate the additive nonparametric components in both the mean and variation functions and derive their convergence rates. The resulting weighted estimators of the linear coefficients in both the mean and variance functions are shown to be asymptotically normal and more efficient than the initial un-weighted estimators. Simulation experiments are conducted to examine the numerical performance of the proposed procedure, which is also applied to analyze the dataset from a nutritional epidemiology study.
KW - Efficiency
KW - Generalized least squares
KW - Heteroscedasticity
KW - Regression spline
KW - Variance function
UR - http://www.scopus.com/inward/record.url?scp=84955450088&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84955450088&origin=recordpage
U2 - 10.1214/15-EJS1080
DO - 10.1214/15-EJS1080
M3 - 21_Publication in refereed journal
VL - 9
SP - 2793
EP - 2827
JO - Electronic Journal of Statistics
JF - Electronic Journal of Statistics
SN - 1935-7524
IS - 2
ER -