December 14, 2018
11:00 a.m.
Louvain-la-Neuve
CORE, room b-135
Joint with ISBA
New approach to distribution-free testing for linearity of regression.
Related topics and extensions
Estate Khmaladze, University of Wellington, NZ
Consider the classical problem that in the pairs $(X_i,Y_i)$, the response variables $Y_i$ have linear regression $a+bX_i$ on the regressors (or explanatory variables)
$X_i$.
The regression empirical process, as we know, is based on residuals $Y_i - \hat a - \hat bX_i$ where we have statistical estimations of the regression parameters. All tests for testing
that the linear regression is true are based on these residuals, or, better, on the regression emirical process. However, the asymptotic distribution of this process depends on the set
of covariates $X_1,\dots, X_n$. Therefore, asymptotic distribution fo the tests statistics has to be calculated every time anew.
The aim of the talk is to describe an unexpectedly simple-looking transformation of the regression empirical process to another process, with the asymptotic distribution free (independent) from the covariates. The transformation is one-to-one, so that no information is lost, and easy to implement.
The transformation is a particular corollary of the general approach, which we describe at the beginning. The same approach works in many parts of testing theory. It certainly works
for general parametric regression problems, as we describe it towards the end of the talk.
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