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

  • Authors:

  • Wolfgang Polonik;Zailong Wang

  • Affiliations:

  • Department of Statistics, University of California, One Shields Ave., Davis, CA 95616, USA;Department of Statistics, University of California, One Shields Ave., Davis, CA 95616, USA

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2005

Quantified Score

Hi-index 0.00

Visualization

Abstract

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.