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On bandwidth choice in nonparametric regression with both short- and long-range dependent errors. (English) Zbl 0856.62041
Summary: 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 band-widths. Nevertheless, the block bootstrap has far better empirical properties, particularly under long-range dependence.

MSC:
62G07 Density estimation
62G09 Nonparametric statistical resampling methods
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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[25] AUSTRALIAN NATIONAL UNIVERSITY AMES, IOWA 80011 G.P.O. BOX 4
[26] CANBERRA, ACT 0200 AUSTRALIA
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