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Expansions And Asymptotics for Statistics - 9781584885900

Un libro in lingua di Small Christopher G. edito da Chapman & Hall, 2010

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For students and researchers who are not specialists in asymptotics, Small draws from his lectures to graduate students in statistics at the U. of Waterloo, Canada, to illustrate how asymptotics, when combined with numerical methods, can be used in probability and statistics. He discusses the role of expansions and asymptotics in statistics, the basic properties of power series and asymptotic series, the study of rational approximations to functions, and various applications, such as the use of the delta method for bias reduction, variance stabilization, and the construction of normalizing transformations, with a focus on asymptotic normality and efficiency of standard estimators. Also covered are theories from the work of Fisher, Cranér, Le Cam, and others; the connection between saddle-point approximation and the Laplace method; and series convergence and the acceleration of that convergence. The basics of mathematical statistics is assumed, including the basic distributions, their properties, and their generating functions. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)

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