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Test for Discontinuities in Nonparametric Regression
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 Title & Authors
Test for Discontinuities in Nonparametric Regression
Park, Dong-Ryeon;
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The difference of two one-sided kernel estimators is usually used to detect the location of the discontinuity points of regression function. The large absolute value of the statistic imply discontinuity of regression function, so we may use the difference of two one-sided kernel estimators as the test statistic for testing null hypothesis of a smooth regression function. The problem is, however, we only know the asymptotic distribution of the test statistic under and we hardly expect the good performance of test if we rely solely on the asymptotic distribution for determining the critical points. In this paper, we show that if we adjust the bias of test statistic properly, the asymptotic rules hold for even small sample size situation.
Asymptotic distribution;discontinuity points;nonparametric regression;
 Cited by
Gijbels, I. and Goderniaux, A. (2004a). Bootstrap test for change-points in nonparametric regression, Journal of Nonparametric Statistics, 16, 591-611 crossref(new window)

Gijbels, I. and Goderniaux, A. C. (2004b). Bandwidth selection for changepoint estimation in nonparametric regression, Technometics, 46, 76-86 crossref(new window)

Muller, H. G. and Stadtmuller, U. (1999). Discontinuous versus smooth regression, The Annals of Statistics, 27, 299-337 crossref(new window)

Qiu, P. (2005). Image Processing and Jump Regression Analysis, John Wiley & Sons, New Jersey

Wu, J. S. and Chu, C. K. (1993). Kernel type estimators of jump points and values of a regression function, The Annals of Statistics, 21, 1545-1566 crossref(new window)