Statistics and Its Interface

Volume 6 (2013)

Number 3

Direction estimation in the single-index model with missing values

Pages: 379 – 385

DOI: http://dx.doi.org/10.4310/SII.2013.v6.n3.a8

Authors

Yuexiao Dong (Temple University, Philadelphia, Pennsylvania, U.S.A.)

Liping Zhu (School of Statistics and Management, Shanghai University of Finance and Economics and the Key Laboratory of Mathematical Economics, Ministry of Education, Shanghai, China)

Abstract

We cast direction estimation in the single-index model into the sufficient dimension reduction framework. Existing sufficient dimension reduction literature with missing values mainly focuses on sliced inverse regression and requires the missing at random (MAR) assumption. In this paper, we propose new methods to handle missing data based on sliced average variance estimation and directional regression. By examining different missingness schemes, we demonstrate that inverse probability weighted estimators for missing predictor are not sensitive to the MAR assumption. The fusionrefined procedures for missing response, on the other hand, may be outperformed by complete case analysis if the response is missing completely at random (MCAR).

Keywords

directional regression, missing at random, missing completely at random, sliced average variance estimation, sliced inverse regression

2010 Mathematics Subject Classification

60K35

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