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Titlebook: Estimation in Semiparametric Models; Some Recent Developm Johann Pfanzagl Book 1990 Springer-Verlag Berlin Heidelberg 1990 DEX.boundary ele

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书目名称Estimation in Semiparametric Models
副标题Some Recent Developm
编辑Johann Pfanzagl
视频videohttp://file.papertrans.cn/316/315783/315783.mp4
丛书名称Lecture Notes in Statistics
图书封面Titlebook: Estimation in Semiparametric Models; Some Recent Developm Johann Pfanzagl Book 1990 Springer-Verlag Berlin Heidelberg 1990 DEX.boundary ele
描述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.
出版日期Book 1990
关键词DEX; boundary element method; development; distribution; eXist; estimator; function; functional; measure; med
版次1
doihttps://doi.org/10.1007/978-1-4612-3396-1
isbn_softcover978-0-387-97238-1
isbn_ebook978-1-4612-3396-1Series ISSN 0930-0325 Series E-ISSN 2197-7186
issn_series 0930-0325
copyrightSpringer-Verlag Berlin Heidelberg 1990
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Power Electronics and Power Systems say {.}: ϑ ∈ Θ, one can usually do better by estimating ϑ first, say by ϑ.(.), and using ∫ . . .(.) (.) as an estimate for ∫ .(.). There is an “intermediate” range, where we know something about the unknown probability measure ., but less than parametric theory takes for granted.
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F.S. Porter,G.V. Brown,J. Cottames the following presentation more transparent. It is justified by the fact that the problem of estimating an .-dimensional functional simply is the problem of estimating its . (1-dimensional) components. (The essential point: componentwise as. efficiency implies joint as. efficiency. See I ., p. 159, Corollary 9.3.6.)
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Introduction say {.}: ϑ ∈ Θ, one can usually do better by estimating ϑ first, say by ϑ.(.), and using ∫ . . .(.) (.) as an estimate for ∫ .(.). There is an “intermediate” range, where we know something about the unknown probability measure ., but less than parametric theory takes for granted.
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Tangent spaces and gradientses the following presentation more transparent. It is justified by the fact that the problem of estimating an .-dimensional functional simply is the problem of estimating its . (1-dimensional) components. (The essential point: componentwise as. efficiency implies joint as. efficiency. See I ., p. 159, Corollary 9.3.6.)
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Refrigeration and Liquefaction,Equipped with the concepts of “tangent space” and “gradient” we now turn to the problem of estimating the functional К, based on an i.i.d. sample .,...,. generated by some . ∈ ..
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