Parametric Inference on the Mean of Functional Data Applied to Lifetime Income Curves

Jin Seo Cho (), Peter Phillips and Juwon Seo
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Juwon Seo: National Univ of Singapore

No 2019rwp-153, Working papers from Yonsei University, Yonsei Economics Research Institute

Abstract: We propose a framework for estimation of the conditional mean function in a parametric model with function space covariates. The approach employs a functional mean squared error objective criterion and allows for possible model misspecification. Under regulatory conditions, consistency and asymptotic normality are established. The analysis extends to situations where the asymptotic properties are influenced by estimation errors arising from the presence of nuisance parameters. Wald, Lagrange multiplier, and quasi-likelihood ratio statistics are studied and asymptotic theory is provided. These procedures enable inference about curve shapes in the observed functional data. Several model specifications where our results are useful are analyzed, including random coefficient models, distributional mixtures, and copula mixture models. Simulations exploring the finite sample properties of our methods are provided. An empirical application conducts lifetime income path comparisons across different demographic groups according to years of work experience. Gender and education levels produce differences in mean income paths corroborating earlier research. However, the mean income paths are found to be proportional so that, upon rescaling, the paths match over gender and across education levels.

Keywords: Functional data; Mean function; Wald test statistic; Lagrange multiplier test statistic; Quasi-likelihood ratio test statistic. (search for similar items in EconPapers)
JEL-codes: C11 C12 C80 (search for similar items in EconPapers)
Pages: 66pages
Date: 2019-11
New Economics Papers: this item is included in nep-ecm, nep-ore and nep-sea
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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