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Expansions of Distributions of Statitics Admitting Stochastic Expansions

  • Rabi Bhattacharya
  • Manfred Denker
Chapter
Part of the DMV Seminar book series (OWS, volume 14)

Abstract

Let X1, X2,..., X n be i.i.d. observations defined on a probability space (Ω, F, P) with values in m ,f1,...,f k real valued measurable functions on m . Many statistics are of the form
$$ H(\bar{Z}) $$
(2.1)
, where H = (H1,..., H p ) is a Borel measurable function on k into p , and
$$ \bar{Z}: = \frac{1}{n}\sum\limits_{{j = 1}}^n {{Z_j},{Z_j}: = ({f_1}({X_j}),...,{f_k}({X_j})) = (Z_j^{{(1)}},...,Z_j^{{(k)}})(1 \leqslant j \leqslant n)} $$
(2.2)
Write
$$ \mu : = E{Z_j} = (E{f_1}({X_j}),...,E{f_k}({X_j})) $$
(2.3)
, V:= dispersion matrix of Z j .

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Copyright information

© Birkhäuser Verlag Basel 1990

Authors and Affiliations

  • Rabi Bhattacharya
    • 1
  • Manfred Denker
    • 2
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Institut für MathematischeStochastikGöttingenGermany

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