Estimating Mixture of Gaussian Processes by Kernel Smoothing

26 Pages Posted: 19 Nov 2013

See all articles by Mian Huang

Mian Huang

Shanghai University of Finance and Economics

Runze Li

Pennsylvania State University

Hansheng Wang

Peking University - Guanghua School of Management

Weixin Yao

Kansas State University

Date Written: November 18, 2013

Abstract

When the functional data are not homogeneous, e.g., there exist multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this paper, we propose a new estimation procedure for the Mixture of Gaussian Processes, to incorporate both functional and inhomogeneous 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 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.

Keywords: Identifiability, EM Algorithm, Kernel Regression, Gaussian Process, Functional Principal Component Analysis

JEL Classification: C10, C13

Suggested Citation

Huang, Mian and Li, Runze and Wang, Hansheng and Yao, Weixin, Estimating Mixture of Gaussian Processes by Kernel Smoothing (November 18, 2013). Available at SSRN: https://ssrn.com/abstract=2356155 or http://dx.doi.org/10.2139/ssrn.2356155

Mian Huang

Shanghai University of Finance and Economics ( email )

777 Guoding Road
Shanghai, AK Shanghai 200433
China

Runze Li

Pennsylvania State University ( email )

University Park
State College, PA 16802
United States

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

Weixin Yao

Kansas State University ( email )

Manhattan, KS 66506-4001
United States

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