Efficient Estimation in a Heteroskedastic Single-Index Model

• Activity Number: 28
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Junli Lin*
• Companies: Penn State
• Keywords: Single-index model ; Heteroscedascity ; Semi-parametric

Abstract

Heteroskedasticity is a common feature in real data. In this paper, a heteroscedastic single-index model is considered. Unlike existing literature, the conditional variance function may depend on a different direction of the predictors from the conditional mean. A two-step estimator of the direction of the conditional mean function is proposed. It involves estimating the conditional variance function, and using it to obtain a weighted semiparametric least squares (WSLS) estimator of the conditional mean function. The asymptotic theory for the proposed WSLS estimator has been established under general conditions. The superiority of the proposed WSLS estimator for moderate sample sizes is suggested by numerical results.