Estimation in Semiparametric Models by Johann Pfanzagl
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.
Johann Pfanzagl completed his degree in Mathematics at the University of Vienna in 1951 as a student of Johann Radon and Edmund Hlawka. After working for several years as a Statistician at the Chamber of Commerce in Austria he became a Professor of Statistics at the University of Vienna in 1959, and at the University of Cologne in 1960. He is one of the few remaining scholars who, in the early days, contributed to the development of statistical theory using sophisticated mathematical tools.
| SKU | Unavailable |
| ISBN 13 | 9780387972381 |
| ISBN 10 | 0387972382 |
| Title | Estimation in Semiparametric Models |
| Author | Johann Pfanzagl |
| Series | Lecture Notes In Statistics |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer-Verlag New York Inc. |
| Year published | 1990-04-06 |
| Number of pages | 112 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |