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arXiv · 1601.06003

Estimation for single-index and partially linear single-index integrated models

Chaohua Dong·Jiti Gao·Dag Tjøstheim
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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.

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Chaohua Dong, Jiti Gao, Dag Tjøstheim. 2016-01-22. Estimation for single-index and partially linear single-index integrated models. https://doi.org/10.1214/15-aos1372

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