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Double smoothing estimation of the multivariate regression function in nonparametric regression. (English) Zbl 1008.62570
Summary: In the case of the random design nonparametric regression, the double smoothing technique is applied to estimate the multivariate regression function. The proposed estimator has desirable properties in both the finite sample and the asymptotic cases. In the finite sample case, it has bounded conditional (and unconditional) bias and variance. On the other hand, in the asymptotic case, it has the same mean square error as the local linear estimator in J.-Q. Fan [ J. Am. Stat. Assoc. 87, 998-1004 (1992; Zbl 0850.62354), Ann. Stat. 21, 196-216 (1993; Zbl 0773.62029)]. Simulation studies demonstrate that the proposed estimator is better than the local linear estimator, because it has a smaller sample mean integrated square error and gives smoother estimates.
MSC:
62G05 Nonparametric estimation
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