A comparison of higher-order bias kernel density estimators

Jones, M. C. and Signorini, D. F. (1997). A comparison of higher-order bias kernel density estimators. Journal of the American Statistical Associatio, 92(439) pp. 1063–1073.

DOI: https://doi.org/10.1080/01621459.1997.10474062

URL: http://www.jstor.org/stable/2965571

Abstract

We consider many kernel-based density estimators, all theoretically improving bias from O(h²), as the smoothing parameter h → 0, to O(h⁴). Examples include higher-order kernels, variable kernel methods, and transformation and multiplicative bias-correction approaches. We stress the similarities between what appear to be disparate approaches. In particular, we show how the mean squared errors of all methods have the same form. Our main practical contribution is a comparative simulation study that isolates the most promising approaches. It remains debatable, however, as to whether even the best methods give worthwhile improvements, at least for small-to-moderate sample exploratory purposes.

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About

• Item ORO ID
• 24107
• Item Type
• Journal Item
• ISSN
• 1537-274X
• Keywords
• bias reduction; higher-order kernel; multiplicative bias correction; smoothing; transformation; variable band- width; variable location
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 1997 American Statistical Association
• Depositing User
• Sarah Frain