Abstract
Let (X, A) be a measurable space, and P a family of probability measures (for short: p-measures) P|A. We consider the problem of estimating the value of a functional К: P → ℝ, based on an i.i.d. sample (x1,..., xn), i.e. a realization from Pn, for some P ∈ P. The restriction to 1-dimensional functional makes the following presentation more transparent. It is justified by the fact that the problem of estimating an m-dimensional functional simply is the problem of estimating its m (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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© 1990 Springer-Verlag Berlin Heidelberg
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Pfanzagl, J. (1990). Tangent spaces and gradients. In: Estimation in Semiparametric Models. Lecture Notes in Statistics, vol 63. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3396-1_2
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DOI: https://doi.org/10.1007/978-1-4612-3396-1_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97238-1
Online ISBN: 978-1-4612-3396-1
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