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Abstract: In this paper, we study the estimation for a partial-linear single-indexmodel. A two-stage estimation procedure is proposed to estimate the linkfunction for the single index and the parameters in the single index, as wellas the parameters in the linear component of the model. Asymptotic normality isestablished for both parametric components. For the index, a constrainedestimating equation leads to an asymptotically more efficient estimator thanexisting estimators in the sense that it is of a smaller limiting variance. Theestimator of the nonparametric link function achieves optimal convergencerates; and the structural error variance is obtained. In addition, the resultsfacilitate the construction of confidence regions and hypothesis testing forthe unknown parameters. A simulation study is performed and an application to areal dataset is illustrated. The extension to multiple indices is brieflysketched.

Author: Jane-Ling Wang, Liugen Xue, Lixing Zhu, Yun Sam Chong


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