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Joe, H. & Maydeu-Olivares, A., 2010. A general family of limited information goodness-of-fit statistics for multinomial data D. Kurowicka & Joe, H. , eds. Dependence Modeling: Vine Copula Handbook, 75, pp.393-419. Available at: {http://www.worldscibooks.com/economics/7699.html doi = 10.1142/9789814299886, @InCollectionCooke.Joe.ea2011.
Joe, H. & Maydeu-Olivares, A., 2006. On the asymptotic distribution of Pearson's $X^2$ in cross-validation samples. Psychometrika, 71, pp.587-592.