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Article

Empirical likelihood based inference for varying coefficient panel data models with fixed effect

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Pages 4973-4990 | Received 31 May 2020, Accepted 22 Sep 2020, Published online: 08 Oct 2020
 

Abstract

In this paper, the empirical likelihood-based inference is investigated with varying coefficient panel data models with fixed effect. A naive empirical likelihood ratio is firstly proposed after the fixed effect is corrected. The maximum empirical likelihood estimators for the coefficient functions are derived as well as their asymptotic properties. Wilk’s phenomenon of this naive empirical likelihood ratio is proven under a undersmoothing assumption. To avoid the requisition of undersmoothing and perform an efficient inference, a residual-adjusted empirical likelihood ratio is further suggested and shown as having a standard chi-square limit distribution, by which the confidence regions of the coefficient functions are constructed. Another estimators for the coefficient functions, together with their asymptotic properties, are considered by maximizing the residual-adjusted empirical log-likelihood function under an optimal bandwidth. The performances of these proposed estimators and confidence regions are assessed through numerical simulations and a real data analysis.

Additional information

Funding

This work is supported by the National Social Science Foundation of China (No. 17BTJ026).

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