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

Which is a manifestation of the well-known circular law for these matrices; but the circular law only captures the macroscopic structure of the spectrum, whereas the asymptotic (1) describes the microscopic structure. This book is an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. Van der Vaart, Asymptotic Statistics, Cambridge University Press, 2000 2. Now I can get to the real topic of the post, which is: finite sample bounds versus asymptotic approximations. STATISTICS DECLARES WAR ON MACHINE LEARNING! 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. Csiszár, Sanov property, generalized I-projection and a conditional limit theorem, The Annals of Probability, 1984, Vol. Charles Knessl1 and Haishen Yao2. Prior research has shown that the G statistic is asymptotically normal under weak regularity conditions. On the Nonsymmetric Longer Queue Model: Joint Distribution, Asymptotic Properties, and Heavy Traffic Limits. 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. Two test statistics, a Difference Test (DT) and a Lagrange multiplier (LM)-type test, are proposed and their asymptotic distributions are derived. Well I hope the dramatic title caught your attention.