Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/66312 
Year of Publication: 
1997
Series/Report no.: 
SFB 373 Discussion Paper No. 1997,76
Publisher: 
Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, Berlin
Abstract: 
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.
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

Files in This Item:
File
Size
386.27 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.