Titlebook: Series Approximation Methods in Statistics; John E. Kolassa Book 19972nd edition Springer Science+Business Media New York 1997 Calc.bounda

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Asymptotics in General,stributions of random variables, including theorems concerning convergence almost surely, to many questions in applied statistics. Le Cam (1969) treats asymptotics from a decision-theoretic viewpoint. Barndorff-Nielsen and Cox (1989) present many applications of the density and distribution function

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Characteristic Functions and the Berry-Esseen Theorem,unction to be reconstructed from the characteristic function are presented. Results are also derived outlining the sense in which inversion of an approximate characteristic function leads to an approximate density or distribution function. These results are applied to derive Berry-Esseen theorems qu

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Saddlepoint Series for Densities,ximations are useful, for example, in constructing tests and confidence intervals, and for calculating .-values. Edgeworth series converge uniformly quickly over the entire possible range of the random variable, when error is measured in an absolute sense. Often times, relative error behavior is mor

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Saddlepoint Series for Distribution Functions,or the density is a linear combination of derivatives of the normal distribution function, and hence is easily integrated to give a corresponding cumulative distribution function approximation. This cumulative distribution function approximation inherits many good properties from the density approxi

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Multivariate Expansions,ed with reference to characteristic functions and cumulant generating functions, and hence these will be defined first. Subsequently Edgeworth density approximations will be defined. Just as in the univariate case, the Edgeworth approximation to probabilities that a random vector lies in a set is th

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Applications to Wald, Likelihood Ratio, and Maximum Likelihood Statistics,imum likelihood estimators, likelihood ratio statistics, and Wald statistics. Bartlett’s correction for the distribution of likelihood ratio statistics is derived. Approximate ancillarity is also discussed.

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Computational Aids,r are comments. . here is generally in the same order as it appears in the text, except that generally lattice material in the text was at the end of chapters; here it follows more naturally immediately . the continuous analogues. Code presented here is the minimal code necessary to perform many of

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