Detecting discontinuities in nonparametric regression curves and surfaces Authors A. W. Bowman Department of Statistics University of Glasgow A. Pope B. Ismail Department of Statistics Mangalore University Article

Received: 01 December 2004 Accepted: 01 June 2006 DOI :
10.1007/s11222-006-9618-y

Cite this article as: Bowman, A.W., Pope, A. & Ismail, B. Stat Comput (2006) 16: 377. doi:10.1007/s11222-006-9618-y
Abstract The existence of a discontinuity in a regression function can be inferred by comparing regression estimates based on the data lying on different sides of a point of interest. This idea has been used in earlier research by Hall and Titterington (1992), Müller (1992) and later authors. The use of nonparametric regression allows this to be done without assuming linear or other parametric forms for the continuous part of the underlying regression function. The focus of the present paper is on assessing the evidence for the presence of a discontinuity within a regression function through examination of the standardised differences of ‘left’ and ‘right’ estimators at a variety of covariate values. The calculations for the test are carried out through distributional results on quadratic forms. A graphical method in the form of a reference band to highlight the sources of the evidence for discontinuities is proposed. The methods are also developed for the two covariate case where there are additional issues associated with the presence of a jump location curve. Methods for estimating this curve are also developed. All the techniques, for the one and two covariate situations, are illustrated through applications.

Keywords Break point Discontinuity Jump location curve Local linear Nonparametric regression Quadratic forms Download to read the full article text

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