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We propose a novel nonparametric regression framework subject to the positivedefiniteness constraint. It offers a highly modular approach for estimatingcovariance functions of stationary processes. Our method can impose positivedefiniteness, as well as isotropy and monotonicity, on the estimators, and itshyperparameters can be decided using cross validation. We define our estimatorsby taking integral transforms of kernel-based distribution surrogates. We thenuse the iterated density estimation evolutionary algorithm, a variant ofestimation of distribution algorithms, to fit the estimators. We also extendour method to estimate covariance functions for point-referenced data. Comparedto alternative approaches, our method provides more reliable estimates forlong-range dependence. Several numerical studies are performed to demonstratethe efficacy and performance of our method. Also, we illustrate our methodusing precipitation data from the Spatial Interpolation Comparison 97 project.

Positive definite nonparametric regression using an evolutionary algorithm with application to covariance function estimation