Adaptive profile-empirical-likelihood inferences for generalized single-index models

作者：Huang, Zhensheng^*; Pang, Zhen; Zhang, Riquan

来源：Computational Statistics & Data Analysis, 2013, 62: 70-82.

DOI：10.1016/j.csda.2012.12.006

• Adaptive empirical likelihood
• Confidence interval
• Generalized single-index model
• Link function
• QLMELE

We study generalized single-index models and propose an efficient equation for estimating the index parameter and unknown link function, deriving a quasi-likelihood-based maximum empirical likelihood estimator (QLMELE) of the index parameter. We then establish an efficient confidence region for any components of the index parameter using an adaptive empirical likelihood method. A pointwise confidence interval for the unknown link function is also established using the QLMELE. Compared with the normal approximation proposed by Cui et al. [Ann Stat. 39 (2011) 16581, our approach is more attractive not only theoretically but also empirically. Simulation studies demonstrate that the proposed method provides smaller confidence intervals than those based on the normal approximation method subject to the same coverage probabilities. Hence, the proposed empirical likelihood is preferable to the normal approximation method because of the complicated covariance estimation. An application to a real data set is also illustrated.

• 出版日期2013-6
• 单位华东师范大学; 南京大学; 南阳理工学院