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The smooth Colonel meets the Reverend

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Kernel smoothing techniques have attracted much attention and some notoriety in recent years. The attention is well deserved as kernel methods free researchers from having to impose rigid parametric structure on their data. The notoriety arises from the fact that the amount of smoothing (i.e., local averaging) that is appropriate for the problem at hand is under the control of the researcher. In this study we provide a deeper understanding of kernel smoothing methods for discrete data by leveraging the unexplored links between hierarchical Bayes models and kernel methods for discrete processes. Several potentially useful results are thereby obtained, including bounds on when kernel smoothing can be expected to dominate non-smooth (e.g., parametric) approaches in mean squared error and suggestions for thinking about the appropriate amount of smoothing.

Keywords: Bayesian Methods; Kernel estimation; bandwidth selection; hierarchical models; nonparametrics

Document Type: Research Article

Affiliations: 1: Department of Economics and Statistical Science, Cornell University, Ithaca, NY, USA,CREATES, funded by the Danish Science Foundation, University of Aarhus, Denmark 2: Department of Economics, Kenneth Taylor Hall, McMaster University, Hamilton, ON, Canada

Publication date: July 1, 2009

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