Nonlinear Boosting with Multiple Testing in High-Dimensional Generalised Linear Models with Binary Responses

2026-07-24

AI Summary

This study addresses variable selection for binary-response generalized linear models in high-dimensional settings by proposing a novel method, termed Boosting with Multiple Testing correction (BMT), which integrates multiple testing adjustment within a nonlinear boosting framework. At each iteration, BMT incorporates only the covariate exhibiting the strongest conditional significance while progressively constructing a sparse model through rigorous control of the multiplicity-induced error rate. The approach uniquely embeds a formal multiple hypothesis testing procedure into the boosting paradigm, offering theoretical guarantees of selection consistency and oracle properties for parameter estimation. Empirical evaluations demonstrate that BMT outperforms existing methods in both variable selection accuracy and estimation precision, and it achieves superior out-of-sample predictive performance in forecasting U.S. inflation.

Abstract

This paper proposes a nonlinear boosting with multiple testing (BMT) approach to variable selection in high-dimensional generalised linear models with binary responses. At each stage of the BMT procedure, the model is updated by adding only the most significant covariate, conditional on those already selected in previous stages, while taking into account the multiple testing nature of the problem. It is shown that, under the stated conditions, the BMT procedure selects all covariates whose true coefficients are nonzero, and no other covariates, with probability tending to one. Furthermore, the procedure enjoys an oracle property, in the sense that the post-BMT maximum likelihood estimator of the parameters of the model is asymptotically equivalent to an oracle estimator that knows the correct sparse model in advance. Monte Carlo experiments demonstrate that BMT outperforms competing methods, delivering high covariate-selection accuracy and low parameter estimation error. An empirical example illustrates that BMT delivers a predictive model for the probability that U.S. inflation exceeds a given threshold over a 12-month horizon which has very good out-of-sample performance.

Problem

• high-dimensional
• variable selection
• generalised linear models
• binary responses
• multiple testing

Innovation

• nonlinear boosting
• multiple testing
• high-dimensional GLM
• variable selection
• oracle property