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Statistica Sinica 3(1993), 557-576


NONPARAMETRIC FUNCTION ESTIMATION

AND BANDWIDTH SELECTION FOR

DISCONTINUOUS REGRESSION FUNCTIONS


J. S. Wu and C. K. Chu


Tamkang University and National Tsing Hua University


Abstract: For nonparametric regression, where the regression function has discontinuity points, the kernel regression estimator and cross-validation are known to be affected by discontinuity. This effect is precisely quantified through the mean average square error (MASE) for the kernel regression estimator and a limiting distribution for the cross-validated bandwidth. An approach is proposed to adjust for the effect of discontinuity on kernel regression estimation and bandwidth selection. The resulting kernel regression estimator and cross-validation are further analyzed by the MASE and a limiting distribution, respectively. Simulation studies show that the asymptotic results are applicable to reasonable sample sizes.



Key words and phrases: Nonparametric regression, kernel regression estimator, cross-validation, discontinuous regression function, mean average square error, asy-mptotic


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