Estimating Mixture of Gaussian Processes by Kernel Smoothing

Mian Huang, Runze Li, Hansheng Wang, Weixin Yao

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

When functional data are not homogenous, for example, when there are multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this article, we propose a new estimation procedure for the mixture of Gaussian processes, to incorporate both functional and inhomogenous properties of the data. Our method can be viewed as a natural extension of high-dimensional normal mixtures. However, the key difference is that smoothed structures are imposed for both the mean and covariance functions. The model is shown to be identifiable, and can be estimated efficiently by a combination of the ideas from expectation-maximization (EM) algorithm, kernel regression, and functional principal component analysis. Our methodology is empirically justified by Monte Carlo simulations and illustrated by an analysis of a supermarket dataset.

Original languageEnglish (US)
Pages (from-to)259-270
Number of pages12
JournalJournal of Business and Economic Statistics
Volume32
Issue number2
DOIs
StatePublished - Apr 3 2014

Fingerprint

Kernel Smoothing
Gaussian Process
Functional Principal Component Analysis
Normal Mixture
Kernel Regression
Functional Data
Covariance Function
estimation procedure
Expectation-maximization Algorithm
Natural Extension
High-dimensional
Monte Carlo Simulation
regression
Curve
simulation
Methodology
methodology
Gaussian process
Kernel smoothing
Model

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty

Cite this

Huang, Mian ; Li, Runze ; Wang, Hansheng ; Yao, Weixin. / Estimating Mixture of Gaussian Processes by Kernel Smoothing. In: Journal of Business and Economic Statistics. 2014 ; Vol. 32, No. 2. pp. 259-270.
@article{03160b5f941641beb83185852b7603b2,
title = "Estimating Mixture of Gaussian Processes by Kernel Smoothing",
abstract = "When functional data are not homogenous, for example, when there are multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this article, we propose a new estimation procedure for the mixture of Gaussian processes, to incorporate both functional and inhomogenous properties of the data. Our method can be viewed as a natural extension of high-dimensional normal mixtures. However, the key difference is that smoothed structures are imposed for both the mean and covariance functions. The model is shown to be identifiable, and can be estimated efficiently by a combination of the ideas from expectation-maximization (EM) algorithm, kernel regression, and functional principal component analysis. Our methodology is empirically justified by Monte Carlo simulations and illustrated by an analysis of a supermarket dataset.",
author = "Mian Huang and Runze Li and Hansheng Wang and Weixin Yao",
year = "2014",
month = "4",
day = "3",
doi = "10.1080/07350015.2013.868084",
language = "English (US)",
volume = "32",
pages = "259--270",
journal = "Journal of Business and Economic Statistics",
issn = "0735-0015",
publisher = "American Statistical Association",
number = "2",

}

Estimating Mixture of Gaussian Processes by Kernel Smoothing. / Huang, Mian; Li, Runze; Wang, Hansheng; Yao, Weixin.

In: Journal of Business and Economic Statistics, Vol. 32, No. 2, 03.04.2014, p. 259-270.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Estimating Mixture of Gaussian Processes by Kernel Smoothing

AU - Huang, Mian

AU - Li, Runze

AU - Wang, Hansheng

AU - Yao, Weixin

PY - 2014/4/3

Y1 - 2014/4/3

N2 - When functional data are not homogenous, for example, when there are multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this article, we propose a new estimation procedure for the mixture of Gaussian processes, to incorporate both functional and inhomogenous properties of the data. Our method can be viewed as a natural extension of high-dimensional normal mixtures. However, the key difference is that smoothed structures are imposed for both the mean and covariance functions. The model is shown to be identifiable, and can be estimated efficiently by a combination of the ideas from expectation-maximization (EM) algorithm, kernel regression, and functional principal component analysis. Our methodology is empirically justified by Monte Carlo simulations and illustrated by an analysis of a supermarket dataset.

AB - When functional data are not homogenous, for example, when there are multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this article, we propose a new estimation procedure for the mixture of Gaussian processes, to incorporate both functional and inhomogenous properties of the data. Our method can be viewed as a natural extension of high-dimensional normal mixtures. However, the key difference is that smoothed structures are imposed for both the mean and covariance functions. The model is shown to be identifiable, and can be estimated efficiently by a combination of the ideas from expectation-maximization (EM) algorithm, kernel regression, and functional principal component analysis. Our methodology is empirically justified by Monte Carlo simulations and illustrated by an analysis of a supermarket dataset.

UR - http://www.scopus.com/inward/record.url?scp=84925945047&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84925945047&partnerID=8YFLogxK

U2 - 10.1080/07350015.2013.868084

DO - 10.1080/07350015.2013.868084

M3 - Article

C2 - 24976675

AN - SCOPUS:84925945047

VL - 32

SP - 259

EP - 270

JO - Journal of Business and Economic Statistics

JF - Journal of Business and Economic Statistics

SN - 0735-0015

IS - 2

ER -