Title page for etd-0626108-135013


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URN etd-0626108-135013
Author Pei-Hsin Chou
Author's Email Address No Public.
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Department Applied Mathematics
Year 2007
Semester 2
Degree Master
Type of Document
Language zh-TW.Big5 Chinese
Title Statistical Inference
Date of Defense 2008-05-30
Page Count 152
Keyword
  • finite population correction factor
  • statistical hypothesis
  • type I error
  • composite hypothesis
  • power
  • Central limit theorem
  • Basu theorem
  • critical value
  • goodness of fit test
  • likelihood ratio test
  • Lehmann-Scheffe theorem
  • complete statistic
  • uniformly minimum variance unbiased estimator
  • ancillary statistic
  • P-value
  • type II error
  • Rao-Blackwell theorem
  • simple hypothesis
  • one-sided test
  • two-sided test
  • significance level
  • sufficient statistic
  • alternative hypothesis
  • testing hypothesis
  • null hypothesis
  • rejection region
  • confidence interval
  • confidence level
  • minimum variance unbiased estimator
  • interval estimation
  • uniformly most powerful test
  • Cramer-Rao inequality
  • likelihood function
  • mean square error
  • moment estimator
  • error of estimation
  • point estimation
  • maximum likelihood estimator
  • bias
  • consistent estimator
  • minimal sufficient statistic
  • factorization theorem
  • unbiased estimator
  • statistic
  • most powerful test
  • test statistics
  • Neyman-Pearson lemma
  • decision rule
  • Abstract In this paper, we will investigate the important properties of three major parts of statistical inference: point estimation, interval estimation and hypothesis testing. For point estimation, we consider the two methods of finding estimators: moment estimators and maximum likelihood estimators, and three methods of evaluating estimators: mean squared error, best unbiased estimators and sufficiency and unbiasedness. For interval estimation, we consider the the general confidence interval, confidence interval in one sample, confidence interval in two samples, sample sizes and finite population correction factors. In hypothesis testing, we consider the theory of testing of hypotheses, testing in one sample, testing in two samples, and the three methods of finding tests: uniformly most powerful test, likelihood ratio test and goodness of fit test. Many examples are used to illustrate their applications.
    Advisory Committee
  • Mong-Na Lo Huang - chair
  • Mei-Hui Guo - co-chair
  • Fu-Chuen Chang - advisor
  • Files
  • etd-0626108-135013.pdf
  • indicate not accessible
    Date of Submission 2008-06-26

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