Oracally Efficient Estimation for Single-Index Link Function with Simultaneous Confidence Band

• Activity Number: 432
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Graphics
• Author(s): Lijie Gu* and Lijian Yang
• Companies: Soochow University and Soochow University
• Keywords: confidence band ; kernel ; link function ; oracle efficiency ; single-index

Abstract

Over the last twenty-five years, various root-n consistent estimators have been devised for the coefficient vector in the popular semiparametric single-index model. In this paper, we prove under general assumptions that kernel estimator of the link function by univariate regression on the index variable is oracally efficient, namely, the estimator with the true single-index coefficient vector is asymptotically indistinguishable from that with any root-n consistent coefficient vector estimator. As a mathematical by product of the oracle efficiency, simultaneous confidence band is constructed for the link function based on the oracally efficient kernel estimator. Simulation experiments corroborate with the theoretical results. The proposed simultaneous confidence band is applied to analyze and test hypothesis about the Boston housing data.