RKHS-based functional nonparametric regression for sparse and irregular longitudinal data

Matthew Avery, Yichao Wu, Hao Zhang, Jiajia Zhang

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This paper focuses on sparse and irregular longitudinal data with a scalar response. The predictor consists of sparse and irregular observations on predictor trajectories, potentially contaminated with measurement errors. For this type of data, Yao, Müller, & Wang (2005a) proposed a principal components analysis through conditional expectation (PACE) approach, which is capable of predicting each predictor trajectory based on sparse and irregular observations. Nonparametric functional data analysis provides an attractive alternative due to its high flexibility. Early work includes functional additive models as in Müller & Yao (2008) and Ferraty & Vieu (2006), which are mainly based on kernel smoothing methods. In this work, we propose a new functional nonparametric regression framework based on reproducing kernel Hilbert spaces (RKHS). The proposed method involves two steps. The first step is to estimate each predictor trajectory based on sparse and irregular observations using PACE. The second step is to conduct a RKHS-based nonparametric regression using the estimated predictor trajectories. Our approach shows improvement over existing methods in simulation studies as well as in a real data example.

Original languageEnglish (US)
Pages (from-to)204-216
Number of pages13
JournalCanadian Journal of Statistics
Volume42
Issue number2
DOIs
StatePublished - 2014

Fingerprint

Reproducing Kernel Hilbert Space
Nonparametric Regression
Longitudinal Data
Irregular
Predictors
Trajectory
Conditional Expectation
Principal Component Analysis
Functional Data Analysis
Kernel Smoothing
Two-step Method
Smoothing Methods
Additive Models
Functional Model
Kernel Methods
Measurement Error
Flexibility
Longitudinal data
Kernel
Hilbert space

Keywords

  • Functional nonparametric regression
  • Longitudinal data
  • RKHS
  • Sparse and irregular

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

RKHS-based functional nonparametric regression for sparse and irregular longitudinal data. / Avery, Matthew; Wu, Yichao; Zhang, Hao; Zhang, Jiajia.

In: Canadian Journal of Statistics, Vol. 42, No. 2, 2014, p. 204-216.

Research output: Contribution to journalArticle

Avery, Matthew ; Wu, Yichao ; Zhang, Hao ; Zhang, Jiajia. / RKHS-based functional nonparametric regression for sparse and irregular longitudinal data. In: Canadian Journal of Statistics. 2014 ; Vol. 42, No. 2. pp. 204-216.
@article{56e48bd148a2422f97953cba2c3b7270,
title = "RKHS-based functional nonparametric regression for sparse and irregular longitudinal data",
abstract = "This paper focuses on sparse and irregular longitudinal data with a scalar response. The predictor consists of sparse and irregular observations on predictor trajectories, potentially contaminated with measurement errors. For this type of data, Yao, M{\"u}ller, & Wang (2005a) proposed a principal components analysis through conditional expectation (PACE) approach, which is capable of predicting each predictor trajectory based on sparse and irregular observations. Nonparametric functional data analysis provides an attractive alternative due to its high flexibility. Early work includes functional additive models as in M{\"u}ller & Yao (2008) and Ferraty & Vieu (2006), which are mainly based on kernel smoothing methods. In this work, we propose a new functional nonparametric regression framework based on reproducing kernel Hilbert spaces (RKHS). The proposed method involves two steps. The first step is to estimate each predictor trajectory based on sparse and irregular observations using PACE. The second step is to conduct a RKHS-based nonparametric regression using the estimated predictor trajectories. Our approach shows improvement over existing methods in simulation studies as well as in a real data example.",
keywords = "Functional nonparametric regression, Longitudinal data, RKHS, Sparse and irregular",
author = "Matthew Avery and Yichao Wu and Hao Zhang and Jiajia Zhang",
year = "2014",
doi = "10.1002/cjs.11215",
language = "English (US)",
volume = "42",
pages = "204--216",
journal = "Canadian Journal of Statistics",
issn = "0319-5724",
publisher = "Statistical Society of Canada",
number = "2",

}

TY - JOUR

T1 - RKHS-based functional nonparametric regression for sparse and irregular longitudinal data

AU - Avery, Matthew

AU - Wu, Yichao

AU - Zhang, Hao

AU - Zhang, Jiajia

PY - 2014

Y1 - 2014

N2 - This paper focuses on sparse and irregular longitudinal data with a scalar response. The predictor consists of sparse and irregular observations on predictor trajectories, potentially contaminated with measurement errors. For this type of data, Yao, Müller, & Wang (2005a) proposed a principal components analysis through conditional expectation (PACE) approach, which is capable of predicting each predictor trajectory based on sparse and irregular observations. Nonparametric functional data analysis provides an attractive alternative due to its high flexibility. Early work includes functional additive models as in Müller & Yao (2008) and Ferraty & Vieu (2006), which are mainly based on kernel smoothing methods. In this work, we propose a new functional nonparametric regression framework based on reproducing kernel Hilbert spaces (RKHS). The proposed method involves two steps. The first step is to estimate each predictor trajectory based on sparse and irregular observations using PACE. The second step is to conduct a RKHS-based nonparametric regression using the estimated predictor trajectories. Our approach shows improvement over existing methods in simulation studies as well as in a real data example.

AB - This paper focuses on sparse and irregular longitudinal data with a scalar response. The predictor consists of sparse and irregular observations on predictor trajectories, potentially contaminated with measurement errors. For this type of data, Yao, Müller, & Wang (2005a) proposed a principal components analysis through conditional expectation (PACE) approach, which is capable of predicting each predictor trajectory based on sparse and irregular observations. Nonparametric functional data analysis provides an attractive alternative due to its high flexibility. Early work includes functional additive models as in Müller & Yao (2008) and Ferraty & Vieu (2006), which are mainly based on kernel smoothing methods. In this work, we propose a new functional nonparametric regression framework based on reproducing kernel Hilbert spaces (RKHS). The proposed method involves two steps. The first step is to estimate each predictor trajectory based on sparse and irregular observations using PACE. The second step is to conduct a RKHS-based nonparametric regression using the estimated predictor trajectories. Our approach shows improvement over existing methods in simulation studies as well as in a real data example.

KW - Functional nonparametric regression

KW - Longitudinal data

KW - RKHS

KW - Sparse and irregular

UR - http://www.scopus.com/inward/record.url?scp=84900033052&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84900033052&partnerID=8YFLogxK

U2 - 10.1002/cjs.11215

DO - 10.1002/cjs.11215

M3 - Article

AN - SCOPUS:84900033052

VL - 42

SP - 204

EP - 216

JO - Canadian Journal of Statistics

JF - Canadian Journal of Statistics

SN - 0319-5724

IS - 2

ER -