# Anton Rask Lundborg - University of Copenhagen

## "Modern methods for variable significance testing"

### Abstract

Testing the significance of a variable or group of variables X for predicting a response Y, given additional covariates Z, is a ubiquitous task in statistics. A simple but common approach is to specify a linear model, and then test whether the regression coefficient for X is non-zero. However, when the model is misspecified, the test may have poor power, for example when X is involved in complex interactions, or lead to many false rejections. In this talk we study the problem of testing the model-free null of conditional mean independence, i.e. that the conditional mean of Y given X and Z does not depend on X. We discuss two recent proposals, one for real-valued Y with a focus on maximising power and another specific to functional X and Y, that are both able to leverage flexible nonparametric or machine learning methods, such as additive models or random forests, to yield both robust error control and high power. The methods come with uniform asymptotic guarantees and numerical experiments demonstrate the effectiveness of the approaches both in terms of maintaining Type I error control, and power, compared to several existing approaches.

#### Additional information:

**Speaker**: Anton Rask Lundborg**Time**: Thursday, 22.06.2023, 16:00 - 17:00**Location**: Faculty Lounge, Room 0.036**Further links**:**Organizer**: Statistics Group**Contact**:- Almut Lunkenheimer
- +49 228 73-9228
- ifs@uni-bonn.de