Estimation in Semiparametric Models : Some Recent Developments

Johann Pfanzagl

ISBN 10: 0387972382 / ISBN 13: 9780387972381

Editore: Springer New York, Springer New York, 1990

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Druck auf Anfrage Neuware - Printed after ordering - 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.

Codice articolo 9780387972381

Dati bibliografici

• Titolo: Estimation in Semiparametric Models : Some Recent Developments
• Editore: Springer New York, Springer New York
• Data di pubblicazione: 1990
• Lingua: Inglese
• ISBN 10: 0387972382
• ISBN 13: 9780387972381
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 242 L x 170 A x 7 P (millimetri) 242 millimetri di larghezza per 170 millimetri di altezza per 7 millimetri di profondità
• Peso: 221 grammi

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Riassunto

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. 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).

Contenuti

A Survey of basic theory.- 1. Tangent spaces and gradients.- 2. Asymptotic bounds for the concentration of estimator-sequences.- 3. Constructing estimator―sequences.- 4. Estimation in semiparametric models.- 5. Families of gradients.- 6. Estimating equations.- B Semiparametric families admitting a sufficient statistic.- 7. A special semiparametric model.- 8. Mixture models.- 9. Examples of mixture models.- Example.- Example.- Example.- L Auxiliary results.- References.- Notation index.