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On double-index dimension reduction for partially functional data

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ABSTRACT In this note, we consider the situation where we have a functional predictor as well as some more traditional scalar predictors, which we call the partially functional problem. We… Click to show full abstract

ABSTRACT In this note, we consider the situation where we have a functional predictor as well as some more traditional scalar predictors, which we call the partially functional problem. We propose a semiparametric model based on sufficient dimension reduction, and thus our main interest is in dimension reduction although prediction can be carried out at a second stage. We establish root-n consistency of the linear part of the estimator. Some Monte Carlo studies are carried out as proof of concept.

Keywords: index dimension; dimension; double index; dimension reduction; partially functional

Journal Title: Journal of Nonparametric Statistics
Year Published: 2019

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