LIBRARY

dc.contributor.author | Dyer, Danny D. | en |

dc.date.accessioned | 2010-06-04T13:44:01Z | en |

dc.date.available | 2010-06-04T13:44:01Z | en |

dc.date.issued | 1978-03 | en |

dc.identifier.uri | http://hdl.handle.net/10106/2363 | en |

dc.description.abstract | Let [see pdf for notation] be a family of probability density functions indexed by the parameter [see pdf for notation]. We assume at least one of the [see pdf for notation] is unknown. Based on a random sample of size n from [see pdf for notation], let [see pdf for notation] be two point estimators of the real-valued function [see pdf for notation], where [see pdf for notation] are specified constants, if any. When comparing [see pdf for notation] and [see pdf for notation], it is quite common to examine the ratio of their respective average precisions usually measured by either mean squared error, [see pdf for notation], or mean absolute error, [see pdf for notation], where [see pdf for notation]. If, for example, [see pdf for notation] for some w0' then 02 is said to be more mean squared efficient than [see pdf for notation] at [see pdf for notation]. However, the numerical value of such a ratio provides very limited insight into the actual relative behavior of the two competing estimators. We, therefore, propose a twofold technique for comparing [see pdf for notation] and which essentially determines (a) the "odds" in favor of [see pdf for notation] being closer to [see pdf for notation] than is [see pdf for notation] and (b) the average closeness of [see pdf for notation] to [see pdf for notation] not only when [see pdf for notation] is closer to [see pdf for notation] than is [see pdf for notation] but also when it is not. Closeness to [see pdf for notation] is measured through an absolute error loss function: [see pdf for notation]. Furthermore, joint consideration of these two concepts is shown to provide a basis for determining which of the two estimators, [see pdf for notation] or [see pdf for notation], is preferred in a given situation. An application of these results will be made with regard to the comparison of estimators of certain reliability characteristics in the exponential failure model. | en |

dc.language.iso | en_US | en |

dc.publisher | University of Texas at Arlington | en |

dc.relation.ispartofseries | Technical Report;77 | en |

dc.subject | Exponential failure model | en |

dc.subject | Absolute error loss function | en |

dc.subject | Estimators | en |

dc.subject.lcsh | Decomposition (Mathematics) | en |

dc.subject.lcsh | Statistics | en |

dc.subject.lcsh | Mathematics Research | en |

dc.title | On the Relative Behavior of Point Estimators Based on a Decomposition of Mean Absolute Error | en |

dc.type | Technical Report | en |

dc.publisher.department | Department of Mathematics | en |

Files | Size | Format | View | Description |
---|---|---|---|---|

MathTechReport077.pdf | 645.6Kb |
View/ |