Abstract
In this paper, we consider a single-index varying-coefficient model with application to longitudinal data. In order to accommodate the within-group correlation, we apply the block empirical likelihood procedure to longitudinal single-index varying-coefficient model, and prove a nonparametric version of Wilks’ theorem which can be used to construct the block empirical likelihood confidence region with asymptotically correct coverage probability for the parametric component. In comparison with normal approximations, the proposed method does not require a consistent estimator for the asymptotic covariance matrix, making it easier to conduct inference for the model's parametric component. Simulations demonstrate how the proposed method works.
Highlights
The single-index varying-coefficient model which was proposed by Huang and Zhensheng [1] is a very important tool to explore the dynamic pattern in many complex dynamic systems, such as economics, finance, politics, epidemiology, medical science, and ecology
As mentioned in Gao et al [2], the concept of complex dynamic systems arises in many varieties
Such systems are often concurrent and distributed, because they have to react to various kinds of events, signals, and conditions. They may be characterized by a system with uncertainties, time delays, stochastic perturbations, hybrid dynamics, distributed dynamics, chaotic dynamics, and a large number of algebraic loops
Summary
The single-index varying-coefficient model which was proposed by Huang and Zhensheng [1] is a very important tool to explore the dynamic pattern in many complex dynamic systems, such as economics, finance, politics, epidemiology, medical science, and ecology. The single-index varying-coefficient models is one method that can be used to describe the complex dynamic systems. Empirical likelihood methods have been applied to nonlongitudinal single-index varying-coefficient model. Xue and Wang [9] developed statistical techniques for the unknown coefficient functions and single-index parameters in the single-index varying-coefficient models. They first estimate the nonparametric component via the local linear fitting, construct an estimated empirical likelihood ratio function, and obtain a maximum empirical likelihood estimator for the parametric component. The usual empirical likelihood method cannot be applied, to the single-index longitudinal data model (1) due to correlation within groups. Proof of the main result is relegated to Section 6
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
