Penalized estimation equation for an extended single-index model

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• 作者：Yongjin Li ; Qingzhao Zhang…
• 关键词：Single ; index model ; Penalized estimating equations ; Variable selection ; Oracle property ; Smoothly clipped absolute deviation ; Adaptive lasso
• 刊名：Annals of the Institute of Statistical Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：69
• 期：1
• 页码：169-187
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics, general; Statistics for Business/Economics/Mathematical Finance/Insurance;
• 出版者：Springer Japan
• ISSN：1572-9052
• 卷排序：69

文摘

The single-index model is a useful extension of the linear regression model. Cui et al. (Ann Stat 39:1658–1688, 2011) proposed an estimating function method for the estimation of index vector in an extended single-index model (ESIM). Nevertheless, how to conduct variable selection for ESIM has not been studied. To solve this problem, we penalize the estimating equation with some types of penalty, such as smoothly clipped absolute deviation penalty and adaptive lasso penalty. Under some regularity conditions, the oracle property is established, i.e., the resulting estimator can be as efficient as the oracle estimator, thus we improve the explanatory ability and accuracy of estimator for the ESIM. A novel algorithm is proposed to solve the penalized estimating equation by combining quasi-Fisher scoring type algorithm and MM algorithm. Simulation study and real data application demonstrate the excellent performance of the proposed estimators.