Variance function additive partial linear models

Yixin Fang, Heng Lian, Hua Liang, David Ruppert

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)2793-2827
Number of pages35
JournalElectronic Journal of Statistics
Volume9
Issue number2
DOIs
StatePublished - Aug 19 2015

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Efficiency
  • Generalized least squares
  • Heteroscedasticity
  • Regression spline
  • Variance function

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