Principal varying coefficient estimator for high-dimensional models. Issue 6 (2nd November 2019) - Zhao, Weihua; Zhang, Fode; Wang, Xuejun; Li, Rui; Lian, Heng
ABSTRACT: We consider principal varying coefficient models in the high-dimensional setting, combined with variable selection, to reduce the effective number of parameters in semiparametric modelling. The estimation is based on B-splines approach. For the unpenalized estimator, we establish non-asymptotic bounds of the estimator and then establish the (asymptotic) local oracle property of the penalized estimator, as well as non-asymptotic error bounds. Monte Carlo studies reveal the favourable performance of the estimator and an application on a real dataset is presented.