Abstract
To this point, most of the statistical results in this book concern properties that hold in some exact sense. An estimator is either sufficient or not, unbiased or not, Bayes or not. If exact properties are impractical or not available, statisticians often rely on approximations. This chapter gives several of the most basic results from probability theory used to derive approximations. Several notions of convergence for random variables and vectors are introduced, and various limit theorems are presented. These results are used in this chapter and later to study and compare the performance of various estimators in large samples.
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© 2009 Springer New York
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Keener, R.W. (2009). Large-Sample Theory. In: Theoretical Statistics. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-0-387-93839-4_8
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DOI: https://doi.org/10.1007/978-0-387-93839-4_8
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Publisher Name: Springer, New York, NY
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Online ISBN: 978-0-387-93839-4
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