1997-09-10Buch DOI: 10.18452/3844
Wild Bootstrap Versus Moment-Oriented Bootstrap
We investigate the relative merits of a “moment-oriented” bootstrap method of Bunke (1997) in comparison with the classical wild bootstrap of Wu (1986) in nonparametric heteroscedastic regression situations. The “moment-oriented” bootstrap is a wild bootstrap based on local estimators of higher order error moments that are smoothed by kernel smoothers. In this paper we perform an asymptotic comparison of these two dierent bootstrap procedures. We show that the moment-oriented bootstrap is in no case worse than the wild bootstrap. We consider the cases of bandwidths with MISE-optimal rates and of bandwidths with rates that perform an optimal bootstrap approximation. When the regression function has the same amount of smoothness as the second and the third order error moment, then it turns out that, in the former case, our method better approximates the distribution of the pivotal statistic than the usual wild bootstrap does. The reason for this behavior is the unavoidable bias in nonparametric regression estimation that permits only a suboptimal amount of smoothing in the classical wild bootstrap case. In the latter case we need more smoothness of the error moments to make the moment-oriented bootstrap better than wild bootstrap. These results are applied to the construction of pointwise confidence intervals where we prove that our bootstrap has a superior behavior for equal smoothness of the regression function and error moments.
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