Variance function estimation in regression model via aggregation procedures

Abstract: In the regression problem, we consider the problem of estimating the variance function by the 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 2error both for MS and C aggregations. We evaluate the performance of these two methods in the heteroscedastic model and illustrate their interest in the regression problem with reject option.