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

Wolfgang Polonik and Zailong Wang

Journal of Multivariate Analysis, 2005, vol. 94, issue 2, 227-249

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[set membership, variant]Rd. 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.

Keywords: Consistency; Excess; mass; Regression; contour; cluster; Empirical; processes; Bracketing; numbers; Asymptotic; normality (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (2)

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