title: Estimating Mixture of Gaussian Processes by Kernel Smoothing.
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.
authors: School of Statistics and Management and Key Laboratory of Mathematical Economics at SHUFE, Ministry of Education, Shanghai University of Finance and Economics (SHUFE), Shanghai, 200433, P. R. China.
authors: Mian
authors: M
authors: Huang
authors: Department of Statistics and The Methodology Center, The Pennsylvania State University, University Park, PA 16802-2111.
authors: Runze
authors: R
authors: Li
authors: Department of Business Statistics and Econometrics, Guanghua School of Management, Peking University, Beijing, 100871, P. R. China.
authors: Hansheng
authors: H
authors: Wang
authors: Department of Statistics, Kansas State University, Manhattan, Kansas 66506.
authors: Weixin
authors: W
authors: Yao
keywords: EM algorithm; Functional principal component analysis; Gaussian process; Identifiability; Kernel regression