Partially functional linear regression in high dimensions

Dehan Kong, Kaijie Xue, Fang Yao, Hao Zhang

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

In modern experiments, functional and nonfunctional data are often encountered simultaneously when observations are sampled from random processes and high-dimensional scalar covariates. It is difficult to apply existing methods for model selection and estimation. We propose a new class of partially functional linear models to characterize the regression between a scalar response and covariates of both functional and scalar types. The new approach provides a unified and flexible framework that simultaneously takes into account multiple functional and ultrahigh-dimensional scalar predictors, enables us to identify important features, and offers improved interpretability of the estimators. The underlying processes of the functional predictors are considered to be infinite-dimensional, and one of our contributions is to characterize the effects of regularization on the resulting estimators. We establish the consistency and oracle properties of the proposed method under mild conditions, demonstrate its performance with simulation studies, and illustrate its application using air pollution data.

Original languageEnglish (US)
Pages (from-to)147-159
Number of pages13
JournalBiometrika
Volume103
Issue number1
DOIs
StatePublished - Jan 1 2015

Fingerprint

Linear regression
Higher Dimensions
Linear Models
Scalar
Air Pollution
air pollution
Air pollution
Random processes
Covariates
Predictors
linear models
Functional Linear Model
Partially Linear Model
Oracle Property
Estimator
Interpretability
Random process
methodology
Model Selection
Regularization

Keywords

  • Functional data
  • Functional linear regression
  • Model selection
  • Principal components
  • Regularization
  • Smoothly clipped absolute deviation

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics
  • Statistics, Probability and Uncertainty

Cite this

Partially functional linear regression in high dimensions. / Kong, Dehan; Xue, Kaijie; Yao, Fang; Zhang, Hao.

In: Biometrika, Vol. 103, No. 1, 01.01.2015, p. 147-159.

Research output: Contribution to journalArticle

Kong, Dehan ; Xue, Kaijie ; Yao, Fang ; Zhang, Hao. / Partially functional linear regression in high dimensions. In: Biometrika. 2015 ; Vol. 103, No. 1. pp. 147-159.
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