Estimating Mixture of Gaussian Processes by Kernel Smoothing

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.