Variance function estimation in regression model via aggregation procedures

Ahmed Zaoui

Journal of Nonparametric Statistics, 2023, vol. 35, issue 2, 397-436

Abstract: In the regression problem, we consider the problem of estimating the variance function by means of aggregation methods. We focus on two particular aggregation setting: Model Selection aggregation (MS) and Convex aggregation (C), where the goal is to select the best candidate and to build the best convex combination of candidates, respectively, among a collection of candidates. In both cases, the construction of the estimator relies on a two-step procedure and requires two independent samples. The first step exploits the first sample to build the candidate estimators for the variance function by the residual-based method and then the second dataset is used to perform the aggregation step. We show the consistency of the proposed method with respect to the $ L^2 $ L2-error both for MS and C aggregations. We evaluate the performance of these two methods in the heteroscedastic model and illustrate their interest in both the regression problem with reject option and the quantile regression.

Date: 2023
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DOI: 10.1080/10485252.2022.2155960

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