Estimation in Semiparametric Models

This PDF book is become immediate popular in Mathematics genre. Estimation in Semiparametric Models is written by famous author Johann Pfanzagl and Ready to Download in ePUB, PDF or Kindle formats. Released by Springer in 1990-04-06. Click Download Book button to get book file and read directly from your devices. Here is a quick description and cover image of Estimation in Semiparametric Models book.

Estimation in Semiparametric Models
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Publisher : Springer
Release Date :
ISBN : 0387972382
Pages : 112 pages
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Estimation in Semiparametric Models by Johann Pfanzagl Book PDF Summary

Assume one has to estimate the mean J x P( dx) (or the median of P, or any other functional t;;(P)) on the basis ofi.i.d. observations from P. Ifnothing is known about P, then the sample mean is certainly the best estimator one can think of. If P is known to be the member of a certain parametric family, say {Po: {) E e}, one can usually do better by estimating {) first, say by {)(n)(.~.), and using J XPo(n)(;r.) (dx) as an estimate for J xPo(dx). There is an "intermediate" range, where we know something about the unknown probability measure P, but less than parametric theory takes for granted. Practical problems have always led statisticians to invent estimators for such intermediate models, but it usually remained open whether these estimators are nearly optimal or not. There was one exception: The case of "adaptivity", where a "nonparametric" estimate exists which is asymptotically optimal for any parametric submodel. The standard (and for a long time only) example of such a fortunate situation was the estimation of the center of symmetry for a distribution of unknown shape.


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