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Estimation in Semiparametric Models: Some Recent Developments

Estimation in Semiparametric Models: Some Recent Developments

Estimation in Semiparametric Models: Some Recent Developments
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Estimation in Semiparametric Models: Some Recent Developments Paperback - 1990

by Pfanzagi, Johann

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Springer Verlag, 1990. Paperback. New. 115 pages. 9.53x6.69x0.28 inches.
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Details

  • Title Estimation in Semiparametric Models: Some Recent Developments
  • Author Pfanzagi, Johann
  • Binding Paperback
  • Edition Softcover reprin
  • Condition New
  • Pages 112
  • Volumes 1
  • Language ENG
  • Publisher Springer Verlag
  • Publication date 1990
  • Bookseller's Inventory # x-0387972382
  • ISBN 9780387972381 / 0387972382
  • Weight 0.45 lbs (0.20 kg)
  • Dimensions 9.61 x 6.69 x 0.25 in (24.41 x 16.99 x 0.64 cm)
  • Category Mathematics
  • Library of Congress subjects Nonparametric statistics, Estimation theory
  • Library of Congress Catalogue Number 90188149
  • Dewey Decimal Code 519.544
  • Quantity available 2

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From the publisher

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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