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Likelihood ratios in asymptotic statistical theory

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Title: Likelihood ratios in asymptotic statistical theory
Author: Leroux, Brian Gilbert
Degree Master of Science - MSc
Program Statistics
Copyright Date: 1985
Subject Keywords Mathematical statistics - Asymptotic theory
Abstract: This thesis deals with two topics in asymptotic statistics. A concept of asymptotic optimality for sequential tests of statistical hypotheses is introduced. Sequential Probability Ratio Tests are shown to have asymptotic optimality properties corresponding to their usual optimality properties. Secondly, the asymptotic power of Pearson's chi-square test for goodness of fit is derived in a new way. The main tool for evaluating asymptotic performance of tests is the likelihood ratio of two hypotheses. In situations examined here the likelihood ratio based on a sample of size ⁿ has a limiting distribution as ⁿ → ∞ and the limit is also a likelihood ratio. To calculate limiting values of various performance criteria of statistical tests the calculations can be made using the limiting likelihood ratio.
URI: http://hdl.handle.net/2429/24843
Series/Report no. UBC Retrospective Theses Digitization Project [http://www.library.ubc.ca/archives/retro_theses/]
Scholarly Level: Graduate

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