# Kollokvium: Distribution-free approach to testing linear regression

- Date:
- Location: Ångströmlaboratoriet, Lägerhyddsvägen 1
- Lecturer: Estate Khmaladze
- Contact person: Thomas Kragh
- Seminarium

Abstract: It very well may be that what we present is one of the very few existing approaches to the problem. The problem is the following:

How do we test that the regression of $Y$ on $X$ is really linear? The tests we want should have asymptotic distribution, free from covariates.

Moreover, we are looking, if possible, for the form of the regression empirical process, which has asymptotic distribution that is independent of or free from covariates. If we can find it, then we have indeed found the whole class of distribution-free tests: these will be tests with statistics based on our form of the regression empirical process.

The mathematics needed to appreciate the talk will be extremely simple — we hardly will need more than one or two sums. However, the mathematical foundation is not that trivial. We will start by explaining the mathematical root of the approach.

The approach will be extended to a very general form of parametric regression — for example, to polynomial regression.