ESTIMATION FOR SINGLE-INDEX AND PARTIALLY LINEAR SINGLE-INDEX INTEGRATED MODELS

• 成果类型: Article
• 署名作者: Dong, Chaohua; Gao, Jiti; Tjostheim, Dag
• 署名单位: Southwestern University of Finance & Economics - China; Monash University; University of Bergen
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1372
• 发表日期: 2016
• 页码: 425-453
• 关键词: nonparametric cointegrating regression; time-series; binary choice; Nonstationarity; likelihood

摘要

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.