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Title:A simple bootstrap method for constructing nonparametric confidence bands for functions PDF Logo
Authors:Hall, Peter
Horowitz, Joel
Issue Date:2012
Series/Report no.:cemmap working paper CWP14/12
Abstract: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 this problem - the fact that the standard bootstrap bias estimator suffers 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 confidnce bands.
Subjects:bandwidth
bias
confidence interval
conservative coverage
coverage error
kernel methods
statistical smoothing
Persistent Identifier of the first edition:doi:10.1920/wp.cem.2012.1412
Document Type:Working Paper
Appears in Collections:cemmap working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies (IFS)

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