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General Asymptotic Confidence Bands Based on Kernel-type Function Estimators

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Abstract

We establish uniform and non-uniform asymptotic simultaneous confidence bands for functionals of the distribution based on kernel-type estimators, which include the Nadaraya-Watson kernel estimators of regression functions and the Akaike-Parzen-Rosenblatt kernel density estimators. Our theorems, based upon functional limit laws derived by modern empirical process theory, allow data-driven local bandwidths for these statistics.

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Authors and Affiliations

  1. L.S.T.A., Université, Pierre et Marie Curie, 7 avenue du Château, F-92340, Bourg-la-Reine, France.

    Paul Deheuvels

  2. Department of Food and Resource Economics, University of Delaware, 206 Townsend Hall, Newark, DE, 19717, U.S.A.

    David M. Mason

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  1. Paul Deheuvels
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  2. David M. Mason
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Deheuvels, P., Mason, D.M. General Asymptotic Confidence Bands Based on Kernel-type Function Estimators. Statistical Inference for Stochastic Processes 7, 225–277 (2004). https://doi.org/10.1023/B:SISP.0000049092.55534.af

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