Abstract:

Estimation in two classes of popular models, single-index models and partially linear single-index models, is studied in this paper. Such models feature nonstationarity. Orthogonal series expansion is used to approximate the unknown integrable link functions in the models and a pro_le approach is used to derive the estimators. The findings include dual convergence rates of the estimators for the single-index models and a trio of convergence rates for the partially linear single index models. Central limit theorem is established for the plug-in estimator of unknown link functions. Monte Carlo simulation verifies these theoretical results. An empirical study furnishes an application of the proposed estimation procedures in practice.

Annals of Statistics, 44，425-453，2016.