Abstract
Let T be a statistical functional defined on a space p of probability measures (p.m.’s) on a locally compact Banach space B. Let X, X1,…, Xn be a sequence of independent and identically distributed (i.i.d.) random variables (r.v.) with common probability P∈P, and let us define \( {P_n}: = {n^{{ - 1}}}\Sigma_{{i = 1}}^n{\delta_{{{X_i}}}} \), the empirical measure, where δXi denotes the Dirac measure at Xi. When T is smooth in a neighborhood of P, a natural estimator of T(P) is its empirical counterpart T(Pn) (see Von Mises (1947), Huber (1981), Manski (1988)).
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© 1995 Springer-Verlag New York, Inc.
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Barbe, P., Bertail, P. (1995). Asymptotic Theory for the Generalized Bootstrap of Statistical Differentiable Functionals. In: The Weighted Bootstrap. Lecture Notes in Statistics, vol 98. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2532-4_2
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DOI: https://doi.org/10.1007/978-1-4612-2532-4_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94478-4
Online ISBN: 978-1-4612-2532-4
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