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For nonparametric regression, where the regression function has discontinuity points, the kernel regression estimator and cross-validation are known to be affected by discontinuity.
ZHIJIAN HE, XIAOQUN WANG, ON THE CONVERGENCE RATE OF RANDOMIZED QUASI-MONTE CARLO FOR DISCONTINUOUS FUNCTIONS, SIAM Journal on Numerical Analysis, Vol. 53, No. 5 (2015), pp. 2488-2503 ...