Iterative weighted estimation based on variance modelling in linear regression models

作者：Zhao, Yan-Yong; Lin, Jin-Guan^*; Huang, Xing-Fang; Wang, Hong-Xia

来源：Communications in Statistics - Simulation and Computation, 2019, 48(9): 2599-2614.

DOI：10.1080/03610918.2018.1458136

• Asymptotic properties
• Linear regression models
• Modified Levenberg-Marquardt method
• Variance modelling

The estimation of variance function plays an extremely important role in statistical inference of the regression models. In this paper we propose a variance modelling method for constructing the variance structure via combining the exponential polynomial modelling method and the kernel smoothing technique. A simple estimation method for the parameters in heteroscedastic linear regression models is developed when the covariance matrix is unknown diagonal and the variance function is a positive function of the mean. The consistency and asymptotic normality of the resulting estimators are established under some mild assumptions. In particular, a simple version of bootstrap test is adapted to test misspecification of the variance function. Some Monte Carlo simulation studies are carried out to examine the finite sample performance of the proposed methods. Finally, the methodologies are illustrated by the ozone concentration dataset.

• 出版日期2019-10-21
• 单位南京审计大学