Data-driven efficient score tests for deconvolution problems

TL;DR

This paper introduces new data-driven score tests for deconvolution problems, enabling hypothesis testing about signal densities with automatic model selection and proven consistency.

Contribution

It develops novel score tests for deconvolution with known and unknown noise densities, incorporating automatic model dimension selection.

Findings

Tests are consistent under the proposed framework.

The approach effectively handles both known and unknown noise densities.

Model selection rules improve test performance and adaptability.

Abstract

We consider testing statistical hypotheses about densities of signals in deconvolution models. A new approach to this problem is proposed. We constructed score tests for the deconvolution with the known noise density and efficient score tests for the case of unknown density. The tests are incorporated with model selection rules to choose reasonable model dimensions automatically by the data. Consistency of the tests is proved.