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Asymptotic expansion in the central limit theorem for quadratic forms
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 81-114 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the statistic of the form $$ Q_n=\sum_{j=1}^N a_{jj}(X_j^2-\mu_2)+\sum_{1\le j\ne k\le N}a_{jk}X_jX_k, $$ where $X_j$ are i.i.d. random variables with the finite sixth moment. We obtain the rate of convergence in the central limit theorem for one term Edgeworth expansion. Furthermore, applications to Toeplitz matrices, quadratic form of ARMA-processes, goodness-of-fit as well as spacing statistics are included. 
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F. Götze; A. N. Tikhomirov; V. A. Yurchenko. Asymptotic expansion in the central limit theorem for quadratic forms. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 11, Tome 341 (2007), pp. 81-114. http://geodesic.mathdoc.fr/item/ZNSL_2007_341_a4/

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