On partial local smoothing rules for curve estimation |
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Authors: | HALL PETER; MARRON J STEPHEN; TITTERINGTON D M |
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Institution: | 1 Centre for Mathematics and its Applications, Australian National University ACT 0200, Canberra, Australia
2 Department of Statistics, University of North Carolina Chapel Hill, North Carolina 27599-3260, USA.
3 Department of Statistics, University of Glasgow, University Gardens Glasgow G12 8QW, UK. |
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Abstract: | We compare the performances of local and global rules for smoothingparameter choice, in terms of asymptotic mean squared errorsof the resulting estimators. In some instances there is surprisinglylittle to choose between local and global approaches; our analysisidentifies contexts where the differences are small or large.This work motivates development of smoothing rules that forma half-way house between local and global smoothing.There, interpolation provides a basis for partial local smoothing.A key result shows that interpolation on even a coarse gridcan produce a very good approximation to full local smoothing.Our theoretical and numerical results lead us to suggest linearinterpolation of a bandwidth obtained by integral approximationson discrete intervals. |
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Keywords: | Adaptive method Bandwidth Global smoothing Kernel method Local linear smoothing Local smoothing Smoothing parameter |
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