Estimation of regression contour clusters—an application of the excess mass approach to regression

The paper shows that the technique known as excess mass can be translated to non-parametric regression with random design in d-dimensional Euclidean space, where the regression function m is given by m ( x ) = E ( Y ∣ X = x ) , x ∈ R d . The approach is applied to estimating regression contour clusters, which are sets where m exceeds a certain threshold value. This is accomplished without prior estimation of the regression function. Consistency of the resulting estimators is studied, and a functional central limit theorem for the excess mass is derived in the regression context.