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arXiv · 2212.03079

Model-Based and Model-Free point prediction algorithms for locally stationary random fields

Srinjoy Das·Yiwen Zhang·Dimitris N. Politis
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Abstract

The Model-free Prediction Principle has been successfully applied to general regression problems, as well as problems involving stationary and locally stationary time series. In this paper we demonstrate how Model-Free Prediction can be applied to handle random fields that are only locally stationary, i.e., they can be assumed to be stationary only across a limited part over their entire region of definition. We construct one-step-ahead point predictors and compare the performance of Model-free to Model-based prediction using models that incorporate a trend and/or heteroscedasticity. Both aspects of the paper, Model-free and Model-based, are novel in the context of random fields that are locally (but not globally) stationary. We demonstrate the application of our Model-based and Model-free point prediction methods to synthetic data as well as images from the CIFAR-10 dataset and in the latter case show that our best Model-free point prediction results outperform those obtained using Model-based prediction.

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Srinjoy Das, Yiwen Zhang, Dimitris N. Politis. 2022-12-06. Model-Based and Model-Free point prediction algorithms for locally stationary random fields. https://arxiv.org/abs/2212.03079

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