On the accuracy of approximate studentization |
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Authors: | D A S Fraser A C M Wong |
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Institution: | (1) Department of Statistics, University of Toronto, M5S 1A1 Toronto, Ontario, Canada;(2) Department of Mathematics and Statistics, York University, M3J 1P3 North York, Ontario, Canada |
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Abstract: | With a parametric model, a measure of departure for an interest parameter is often easily constructed but frequently depends
in distribution on nuisance parameters; the elimination of such nuisance parameter effects is a central problem of statistical
inference. Fraser & Wong (1993) proposed a nuisance-averaging or approximate Studentization method for eliminating the nuisance
parameter effects. They showed that, for many standard problems where an exact answer is available, the averaging method reproduces
the exact answer. Also they showed that, if the exact answer is unavailable, as say in the gamma-mean problem, the averaging
method provides a simple approximation which is very close to that obtained from third order asymptotic theory. The general
asymptotic accuracy, however, of the method has not been examined. In this paper, we show in a general asymptotic context
that the averaging method is asymptotically a second order procedure for eliminating the effects of nuisance parameters. |
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Keywords: | Some" target="_blank">Some Averaging Confidence distribution function Studentization |
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