Estimating Mixture of Gaussian Processes by Kernel Smoothing |
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| Authors: | Mian Huang Runze Li Hansheng Wang Weixin Yao |
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| Institution: | 1. 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 (huang.mian@shufe.edu.cn);2. Department of Statistics and The Methodology Center, The Pennsylvania State University, University Park, PA 16802 (rzli@psu.edu);3. Department of Business Statistics and Econometrics, Guanghua School of Management, Peking University, Beijing 100871, P. R. China (hansheng@gsm.pku.edu.cn);4. Department of Statistics, Kansas State University, Manhattan, KS 66506 (wxyao@ksu.edu) |
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| 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. |
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| Keywords: | EM algorithm Functional principal component analysis Identifiability |
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