In this paper, a new robust and efficient estimation approach based on local modal regression is proposed for partially linear single-index models, of which the univariate nonparametric link function is approximated by local polynomial regression. The asymptotic normality of proposed estimators...

In this work, we redefined two important statistics, the CLRT test [Z. Bai, D. Jiang, J. Yao, S. Zheng, Corrections to LRT on large-dimensional covariance matrix by RMT, The Annals of Statistics 37 (6B) (2009) 3822–3840] and the LW test [O. Ledoit, M. Wolf, Some hypothesis tests for the...