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2021 Consistent regression using data-dependent coverings
Vincent Margot, Jean-Patrick Baudry, Frederic Guilloux, Olivier Wintenberger
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Electron. J. Statist. 15(1): 1743-1782 (2021). DOI: 10.1214/21-EJS1806

Abstract

We introduce a procedure to generate an estimator of the regression function based on a data-dependent quasi-covering of the feature space. A quasi-partition is generated from the quasi-covering and the estimator predicts the conditional empirical expectation over the cells of the quasi-partition. We provide sufficient conditions to ensure the consistency of the estimator. Each element of the quasi-covering is labeled as significant or insignificant. We avoid the condition of cell shrinkage commonly found in the literature for data-dependent partitioning estimators. This reduces the number of elements in the quasi-covering. An important feature of our estimator is that it is interpretable.

The proof of the consistency is based on a control of the convergence rate of the empirical estimation of conditional expectations, which is interesting in itself.

Citation

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Vincent Margot. Jean-Patrick Baudry. Frederic Guilloux. Olivier Wintenberger. "Consistent regression using data-dependent coverings." Electron. J. Statist. 15 (1) 1743 - 1782, 2021. https://doi.org/10.1214/21-EJS1806

Information

Received: 1 September 2019; Published: 2021
First available in Project Euclid: 26 March 2021

Digital Object Identifier: 10.1214/21-EJS1806

Subjects:
Primary: 62G05, 62G08
Secondary: 62G20

JOURNAL ARTICLE
40 PAGES


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Vol.15 • No. 1 • 2021
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