Variance function estimation in regression model via aggregation procedures
This work addresses variance estimation in regression, which is important for statistical modeling and applications like regression with reject option, but it appears incremental as it builds on existing aggregation techniques.
The paper tackles the problem of estimating the variance function in regression models using aggregation methods, specifically Model Selection and Convex aggregation, and shows consistency in L2 error for both approaches.
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.