Jaki, Thomas and West, R. Webster (2008) *Maximum kernel likelihood estimation.* Journal of Computational and Graphical Statistics, 17 (4). pp. 976-993. ISSN 1061-8600

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## Abstract

We introduce an estimator for the population mean based on maximizing likelihoods formed by parameterizing a kernel density estimate. Due to these origins, we have dubbed the estimator the maximum kernel likelihood estimate (mkle). A speedy computational method to compute the mkle based on binning is implemented in a simulation study which shows that the mkle at an optimal bandwidth is decidedly superior in terms of efficiency to the sample mean and other measures of location for heavy tailed symmetric distributions. An empirical rule and a computational method to estimate this optimal bandwidth are developed and used to construct bootstrap confidence intervals for the population mean. We show that the intervals have approximately nominal coverage and have significantly smaller average width than the standard t and z intervals. Lastly, we develop some mathematical properties for a very close approximation to the mkle called the kernel mean. In particular, we demonstrate that the kernel mean is indeed unbiased for the population mean for symmetric distributions.

Item Type: | Article |
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Journal or Publication Title: | Journal of Computational and Graphical Statistics |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 11512 |

Deposited By: | Dr Thomas Jaki |

Deposited On: | 29 Aug 2008 09:57 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 03 Nov 2015 13:50 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/11512 |

### Available Versions of this Item

- Maximum Kernel Likelihood Estimation. (deposited 07 Jul 2008 10:23)
- Maximum kernel likelihood estimation. (deposited 29 Aug 2008 09:57)
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- Maximum kernel likelihood estimation. (deposited 29 Aug 2008 09:57)

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