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# s8 - Stat 5102 Lecture Slides Deck 8 Charles J Geyer School...

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Stat 5102 Lecture Slides Deck 8 Charles J. Geyer School of Statistics University of Minnesota 1

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Plug-In and the Bootstrap The worst mistake one can make in statistics is to confuse the sample and the population or to confuse estimators and param- eters. In short, ˆ θ is not θ . But the plug-in principle (slides 78–84, deck 2 and slides 58– 66 and 97, deck 3) seems to say the opposite. Sometimes it is o. k. to just plug in and estimate for an unknown parame- ter. In particular, it is o. k. to plug in a consistent estimator of the asymptotic variance of a parameter in forming asymptotic confidence intervals for that parameter. So it is a terrible mistake to confuse a parameter of interest and an estimator for it, but it may not be a mistake to ignore the difference between a nuisance parameter and an estimator for it. 2
Plug-In and the Bootstrap (cont.) The “bootstrap” is a cute name for a vast generalization of the plug-in principle. The name comes from the cliche “pull oneself up by one’s boot- straps” which although it describes a literal impossibility actually means succeed by one’s own efforts. In statistics, the hint of impossibility is part of the flavor. The bootstrap seems problematic, but it (usually) works. 3

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The Nonparametric Bootstrap The bootstrap comes in two flavors, parametric and nonpara- metric. We’ll do the latter first. The theory of the nonparametric bootstrap is all above the level of this course, so we give a non-theoretical explanation. The nonparametric bootstrap, considered non-theoretically, is just an analogy.
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s8 - Stat 5102 Lecture Slides Deck 8 Charles J Geyer School...

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