Estimating Mixture of Gaussian Processes by Kernel Smoothing
26 Pages Posted: 19 Nov 2013
Date Written: November 18, 2013
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
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