The Annals of Statistics

On bandwidth choice in nonparametric regression with both short- and long-range dependent errors

Peter Hall, Soumendra Nath Lahiri, and Jörg Polzehl

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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.

Article information

Ann. Statist., Volume 23, Number 6 (1995), 1921-1936.

First available in Project Euclid: 15 October 2002

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Zentralblatt MATH identifier

Primary: 62G07: Density estimation 62G09: Resampling methods
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]

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


Hall, Peter; Lahiri, Soumendra Nath; Polzehl, Jörg. On bandwidth choice in nonparametric regression with both short- and long-range dependent errors. Ann. Statist. 23 (1995), no. 6, 1921--1936. doi:10.1214/aos/1034713640.

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