Nonparametric Inference in Functional Linear Quantile Regression by RKHS Approach

Kosaku Takanashi
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Kosaku Takanashi: Faculty of Economics, Keio University

No 2018-002, Keio-IES Discussion Paper Series from Institute for Economics Studies, Keio University

Abstract: This paper studies an asymptotics of functional linear quantile regression in which the dependent variable is scalar while the covariate is a function. We apply a roughness regularization approach of a reproducing kernel Hilbert space framework. In the above circumstance, narrow convergence with respect to uniform convergence fails to hold, because of the strength of its topology. A new approach we propose to the lack-ofuniform- convergence is based on Mosco-convergence that is weaker topology than uniform convergence. By applying narrow convergence with respect to Mosco topology, we develop an infinite-dimensional version of the convexity argument and provide a proof of an asymptotic normality of argmin processes. Our new technique also provides the asymptotic confidence intervals and the generalized likelihood ratio hypothesis testing in fully nonparametric circumstance.

Keywords: Functional Linear Quantile Regression; Mosco topology; Generalized Likelihood Ratio Test; Estimation with Convex Constraint (search for similar items in EconPapers)
JEL-codes: C12 C14 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2018-03-04
New Economics Papers: this item is included in nep-ecm
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Persistent link: https://EconPapers.repec.org/RePEc:keo:dpaper:2018-002

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