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A central limit theorem for generalized multilinear forms

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  • de Jong, Peter
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    Abstract

    Let X1, ..., Xn be independent random variables and define for each finite subset I [subset of] {1, ..., n} the [sigma]-algebra = [sigma]{Xi : i [epsilon] I}. In this paper -measurable random variables WI are considered, subject to the centering condition E(WI [short parallel] ) = 0 a.s. unless I [subset of] J. A central limit theorem is proven for d-homogeneous sums W(n) = [Sigma][short parallel]I[short parallel] = dWI, with var W(n) = 1, where the summation extends over all (nd) subsets I [subset of] {1, ..., n} of size [short parallel]I[short parallel] = d, under the condition that the normed fourth moment of W(n) tends to 3. Under some extra conditions the condition is also necessary.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 34 (1990)
    Issue (Month): 2 (August)
    Pages: 275-289

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    Handle: RePEc:eee:jmvana:v:34:y:1990:i:2:p:275-289

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    Keywords: martingales d-homogeneous sums Hoeffding decomposition central limit theorem;

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    Cited by:
    1. Gao, Jiti & Hong, Yongmiao, 2007. "Central limit theorems for weighted quadratic forms of dependent processes with applications in specification testing," MPRA Paper 11977, University Library of Munich, Germany, revised Dec 2007.
    2. Fan, Yanqin & Ullah, Aman, 1999. "Asymptotic Normality of a Combined Regression Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 191-240, November.

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