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Asymptotic Statistics A. W. van der Vaart
Publisher: Cambridge University Press

The following is a list of statistics and probability exercises that can be found on Statlect. MR 2798785 (2012b:60019), http://dx.doi.org/10.1070/SM2011v202n02ABEH004142; 7. Getis and Ord's G and Moran's I statistics, as well as their local versions Gi and Ii, have been widely used in spatial data analysis. The one reference I'd recommend is A.W.van der Vaart "Asymptotic Statistics", ch. Abstract: We develop analytic tools for the asymptotics of general trie statistics, which are particularly advantageous for clarifying the asymptotic variance. All exercises are accompanied by fully explained solutions. Wolfowitz's research contains many asymptotic results. Tulyakov, Asymptotic regimes in the saturation zone for C-D-kernels for an ensemble of Meixner orthogonal polynomials, Uspekhi Mat. A more advanced monograph is "Weak Convergence and Empirical Processes" by Wellner and van der Vaart. MR 2220042 (2006m:47057), http://dx.doi.org/10.1016/j.jat.2005.09.006; 34. The estimator from the smooth weighted estimating equations are shown to be consistent and have the same asymptotic distribution as that from the nonsmooth version. Others are large samples of test statistics with asymptotic χ2 distributions. Here is a practical and mathematically rigorous introduction to the field of asymptotic statistics. Prior research has shown that the G statistic is asymptotically normal under weak regularity conditions. Shcherbina, Universality of the local eigenvalue statistics for a class of unitary invariant random matrix ensembles, J. Publisher: Cambridge University Press | ISBN: 0521784506 | edition 2000 | PDF | 462 pages | 21,6 mb.