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

We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive definiteness, as well as isotropy and monotonicity, on the estimators...

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Bibliographic Details
Published in:arXiv.org
Main Author: Kang, Myeongjong
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 25.04.2023
Subjects:
Covariance
Estimation
Estimators
Evolutionary algorithms
Integral transforms
Interpolation
Isotropy
Spatial data
Stationary processes
ISSN:2331-8422
Online Access:Get full text
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Summary:We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive definiteness, as well as isotropy and monotonicity, on the estimators, and its hyperparameters can be decided using cross validation. We define our estimators by taking integral transforms of kernel-based distribution surrogates. We then use the iterated density estimation evolutionary algorithm, a variant of estimation of distribution algorithms, to fit the estimators. We also extend our method to estimate covariance functions for point-referenced data. Compared to alternative approaches, our method provides more reliable estimates for long-range dependence. Several numerical studies are performed to demonstrate the efficacy and performance of our method. Also, we illustrate our method using precipitation data from the Spatial Interpolation Comparison 97 project.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.2304.13168