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December 1995 On bandwidth choice in nonparametric regression with both short- and long-range dependent errors
Peter Hall, Soumendra Nath Lahiri, Jörg Polzehl
Ann. Statist. 23(6): 1921-1936 (December 1995). DOI: 10.1214/aos/1034713640


We analyse methods based on the block bootstrap and leave-out cross-validation, for choosing the bandwidth in nonparametric regression when errors have an almost arbitrarily long range of dependence. A novel analytical device for modelling the dependence structure of errors is introduced. This allows a concise theoretical description of the way in which the range of dependence affects optimal bandwidth choice. It is shown that, provided block length or leave-out number, respectively, are chosen appropriately, both techniques produce first-order optimal bandwidths. Nevertheless, the block bootstrap has far better empirical properties, particularly under long-range dependence.


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Peter Hall. Soumendra Nath Lahiri. Jörg Polzehl. "On bandwidth choice in nonparametric regression with both short- and long-range dependent errors." Ann. Statist. 23 (6) 1921 - 1936, December 1995.


Published: December 1995
First available in Project Euclid: 15 October 2002

zbMATH: 0856.62041
MathSciNet: MR1389858
Digital Object Identifier: 10.1214/aos/1034713640

Primary: 62G07 , 62G09
Secondary: 62M10

Keywords: Bandwidth choice , block bootstrap , Correlated errors , cross-validation , Curve estimation , Kernel estimator , local linear smoothing , long-range dependence , mean squared error , Nonparametric regression , Resampling , short-range dependence

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 6 • December 1995
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