Abstract
Kernel density estimators which allow different amounts of smoothing at different locations are studied. Modifications of estimators proposed by Breiman, Meisel and Purcell (1977) and Abramson (1982a), which have variable window widths, are seen to have very fast rates of convergence. These rates have traditionally been obtained using a less natural higher order kernel, which has the disadvantage of allowing an estimator which takes on negative values.
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Research partially supported by NSF Grants DMS-8400602 and DMS-8701201
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Hall, P., Marron, J.S. Variable window width kernel estimates of probability densities. Probab. Th. Rel. Fields 80, 37–49 (1988). https://doi.org/10.1007/BF00348751
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DOI: https://doi.org/10.1007/BF00348751
Keywords
- Probability Density
- Stochastic Process
- Probability Theory
- Statistical Theory
- Fast Rate