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A0235
Title: Nonparametric operator-regularized covariance function estimation Authors:  Raymond Wong - Iowa State University (United States) [presenting]
Xiaoke Zhang - George Washington University (United States)
Abstract: A class of nonparametric covariance function estimators is developed by utilizing spectral regularization of an operator, which is associated with a typically infinite dimensional reproducing kernel Hilbert space. By construction, these estimators are positive semi-definite and hence valid covariance functions. A related representer theorem is established to provide a finite dimensional representation of such estimators. In order to achieve low-rank estimations, trace-norm regularization is studied in detail. A specific computational algorithm is developed and this estimator is shown to enjoy excellent rates of convergence under either fixed or random designs. The empirical performance of the proposed trace-norm-regularized estimator is demonstrated in a simulation study, while its practical utility is illustrated in an analysis of a traffic data set.