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2015 Variance function additive partial linear models
Yixin Fang, Heng Lian, Hua Liang, David Ruppert
Electron. J. Statist. 9(2): 2793-2827 (2015). DOI: 10.1214/15-EJS1080


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.


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Yixin Fang. Heng Lian. Hua Liang. David Ruppert. "Variance function additive partial linear models." Electron. J. Statist. 9 (2) 2793 - 2827, 2015.


Received: 1 March 2015; Published: 2015
First available in Project Euclid: 31 December 2015

zbMATH: 1329.62199
MathSciNet: MR3439185
Digital Object Identifier: 10.1214/15-EJS1080

Primary: 62G08
Secondary: 62F12 , 62G20 , 62J02

Keywords: efficiency , generalized least squares , Heteroscedasticity , regression spline , variance function

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.9 • No. 2 • 2015
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