Johann Pfanzagl

(Author)

Estimation in Semiparametric Models: Some Recent Developments (Softcover Reprint of the Original 1st 1990)Paperback - Softcover Reprint of the Original 1st 1990, 6 April 1990

Estimation in Semiparametric Models: Some Recent Developments (Softcover Reprint of the Original 1st 1990)
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Part of Series
Lecture Notes in Statistics
Part of Series
Recent Research in Psychology
Print Length
112 pages
Language
English
Publisher
Springer
Date Published
6 Apr 1990
ISBN-10
0387972382
ISBN-13
9780387972381

Description

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.

Product Details

Author:
Johann Pfanzagl
Book Edition:
Softcover Reprint of the Original 1st 1990
Book Format:
Paperback
Country of Origin:
DE
Date Published:
6 April 1990
Dimensions:
24.41 x 16.99 x 0.64 cm
ISBN-10:
0387972382
ISBN-13:
9780387972381
Language:
English
Location:
New York, NY
Pages:
112
Publisher:
Weight:
204.12 gm

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