New Semiparametric Estimation Procedure for Functional Coefficient Longitudinal Data Models

Jia Chen, Degui Li and Yingcun Xia

Discussion Papers from Department of Economics, University of York

Abstract: In order to achieve dimension reduction for the nonparametric functional coefficients and improve the estimation efficiency, in this paper we introduce a novel semiparametric estimation procedure which combines a principal component analysis of the functional coefficients and a Cholesky decomposition of the within-subject covariance matrices. Under some regularity conditions, we derive the asymptotic distribution for the proposed semiparametric estimators and show that the efficiency of the estimation of the (principal) functional coefficients can be improved when the within-subject covariance structure is correctly speci ed. Furthermore, we apply two approaches to consistently estimate the Cholesky decomposition, which avoid a possible misspeci cation of the within-subject covariance structure and ensure the efficiency improvement for the estimation of the (principal) functional coefficients. Some numerical studies including Monte Carlo experiments and an empirical application show that the developed semiparametric method works reasonably well in finite samples.

Keywords: Cholesky decomposition; functional coefficients; local linear smoothing; principal component analysis; profile least squares; within-subject covariance (search for similar items in EconPapers)
JEL-codes: C14 C23 C51 (search for similar items in EconPapers)
Date: 2015-10
New Economics Papers: this item is included in nep-ecm and nep-ore
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