A simple bootstrap method for constructing nonparametric confidence bands for functions
Peter Hall and
Joel L. Horowitz ()
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Peter Hall: Institute for Fiscal Studies
Joel L. Horowitz: Institute for Fiscal Studies and Northwestern University
No CWP29/13, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies
Standard approaches to constructing nonparametric confidence bands for functions are frustrated by the impact of bias, which generally is not estimated consistently when using the bootstrap and conventionally smoothed function estimators. To overcome this problem, it is common practice to either undersmooth, so as to reduce the impact of bias, or oversmooth, and thereby introduce an explicit or implicit bias estimator. However, these approaches and others based on nonstandard smoothing methods, complicate the process of inference, for example by requiring the choice of new, unconventional smoothing parameters and, in the case of undersmoothing, producing relatively wide bands. In this paper we suggest a new approach, which exploits to our advantage one of the difficulties that, in the past, has prevented an attractive solution to the problem— the fact that the standard bootstrap bias estimator suffer from relatively high-frequency stochastic error. The high frequency, together with a technique based on quantiles, can be exploited to dampen down the stochastic error term, leading to relatively narrow, simple-to-construct confidence bands. A supplement to this article, which outlines theoretical properties underpinning the methodology and provides a proof of theorem, can be viewed here
Keywords: bandwidth; bias; boostrap; confidence interval; conservative coverage; coverage error; kernal methods; statistical smoothing (search for similar items in EconPapers)
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