# Aggregated kernel based tests for signal detection in a regression model

## TL;DR

This paper introduces an aggregated kernel-based testing method for detecting signals in regression models, which is effective even with unknown variance and adapts to various alternative hypotheses.

## Contribution

It proposes a novel aggregation approach for kernel-based tests that automatically selects kernels and parameters, ensuring adaptivity and non-asymptotic control.

## Key findings

- The method achieves minimax adaptive testing over multiple classes of alternatives.
- It provides non-asymptotic level-? tests with controlled error rates.
- The aggregation procedure simplifies kernel choice and improves detection power.

## Abstract

Considering a regression model, we address the question of testing the nullity of the regression function. The testing procedure is available when the variance of the observations is unknown and does not depend on any prior information on the alternative. We first propose a single testing procedure based on a general symmetrickernel and an estimation of the variance of the observations. The corresponding critical values are constructed to obtain non asymptotic level-? tests. We then introduce an aggregation procedure to avoid the difficult choice of the kernel and of the parameters of the kernel. The multiple tests satisfy non-asymptotic properties and are adaptive in the minimax sense over several classes of regular alternatives.