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On the Relative Behavior of Point Estimators Based on a Decomposition of Mean Absolute Error

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On the Relative Behavior of Point Estimators Based on a Decomposition of Mean Absolute Error

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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

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