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.
"Consistent regression using data-dependent coverings." Electron. J. Statist. 15 (1) 1743 - 1782, 2021. https://doi.org/10.1214/21-EJS1806