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One of the techniques used in the latest case study (Section 3.7) is an asymptotic expansion of an estimator as well as that for a log-likelihood function. The most well-known asymptotic expansion is the Taylor expansion, which is a mathematical tool, rather than a statistical method. However, the method is used so extensively in both theoretical and applied statistics that its role in statistics can hardly be overstated. Several other expansions, including the Edgeworth expansion and Laplace approximation, can be derived from the Taylor expansion. It should be pointed out that some elementary expansions can also be very useful (see Section 4.5)
KeywordsAsymptotic Expansion Taylor Expansion Central Limit Theorem Fisher Information Matrix Orthonormal System
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