Thresholding tests

TL;DR

This paper introduces a new class of thresholding-based statistical tests for generalized linear models, capable of handling high-dimensional data and improving power and level control over existing methods.

Contribution

It develops novel asymptotically pivotal statistics and an affine lasso extension, enabling new tests for both parametric and nonparametric models with superior performance.

Findings

Thresholding tests outperform existing tests in level control.

The tests show higher power under sparse and dense alternatives.

Simulation results confirm the effectiveness of the proposed methods.

Abstract

We derive a new class of statistical tests for generalized linear models based on thresholding point estimators. These tests can be employed whether the model includes more parameters than observations or not. For linear models, our tests rely on pivotal statistics derived from model selection techniques. Affine lasso, a new extension of lasso, allows to unveil new tests and to develop in the same framework parametric and nonparametric tests. Our tests for generalized linear models are based on new asymptotically pivotal statistics. A composite thresholding test attempts to achieve uniformly most power under both sparse and dense alternatives with success. In a simulation, we compare the level and power of these tests under sparse and dense alternative hypotheses. The thresholding tests have a better control of the nominal level and higher power than existing tests.