Electronic Journal of Statistics

Variance function additive partial linear models

Yixin Fang, Heng Lian, Hua Liang, and David Ruppert

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist., Volume 9, Number 2 (2015), 2793-2827.

Dates
Received: March 2015
First available in Project Euclid: 31 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1451577217

Digital Object Identifier
doi:10.1214/15-EJS1080

Mathematical Reviews number (MathSciNet)
MR3439185

Zentralblatt MATH identifier
1329.62199

Subjects
Primary: 62G08: Nonparametric regression
Secondary: 62G20: Asymptotic properties 62J02: General nonlinear regression 62F12: Asymptotic properties of estimators

Keywords
Efficiency heteroscedasticity generalized least squares regression spline variance function

Citation

Fang, Yixin; Lian, Heng; Liang, Hua; Ruppert, David. Variance function additive partial linear models. Electron. J. Statist. 9 (2015), no. 2, 2793--2827. doi:10.1214/15-EJS1080. https://projecteuclid.org/euclid.ejs/1451577217


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