Abstract
Estimation mainly for two classes of popular models, single-index 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 profile approach is used to derive the estimators. The findings include the dual rate of convergence of the estimators for the single-index models and a trio of convergence rates for the partially linear single-index models. A new central limit theorem is established for a plug-in estimator of the unknown link function. Meanwhile, a considerable extension to a class of partially nonlinear single-index models is discussed in Section 4. Monte Carlo simulation verifies these theoretical results. An empirical study furnishes an application of the proposed estimation procedures in practice.
Original language | English |
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Pages (from-to) | 425-453 |
Number of pages | 29 |
Journal | Annals of Statistics |
Volume | 44 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1 Feb 2016 |
Keywords
- A trio of convergence rates
- Dual convergence rates
- Integrated time series
- Orthogonal series expansion
- Partially linear single-index models
- Single-index models