Mathematical Statistics 1 | MA | Course

Brief Information
  • Name : Mathematical statistics 1
  • Lecturer : 지은숙
  • Semester : 2014 Fall
  • Course : BM. Mathematics
  • Textbook : 여인권, 송문섭, 허문열 (2009) 이론통계. 박영사
  • Syllabus [link]
  • In short
    • Introduction to Statistics.
    • 2-semester course:  Mathematical statistics 1 and Mathematical statistics 2
Trace lectures
Assignments

None

Summarize themes

[After mid-term exam]

  • t-distribution
  • F-distribution
  • Desirable characteristics of estimators
    • Bias
    • Small MSE(Mean Square Error). Big efficiency.
    • Consistency
  • Estimation
    • Point estimation
      • Method of moment estimation
      • Method of maximum likelihood estimation
    • Interval estimation
      • Confidence interval
      • Confidence level
      • Interval estimation in the normal distribution
      • Interval estimation of ratio
        • Limit of error
  • Hypothesis testing
    • Null hypothesis
    • Alternative hypothesis
    • Test statistic
    • Critical region
    • Acceptance region
    • Significance level
    • Type I error
    • Type II error
    • p-value
    • Significance probability
    • Simple hypothesis
    • Composite hypothesis
    • Power function
    • Power
    • One-sided test
    • Two-sided test
    • Randomized test and Non-randomized test
    • Test function. Critical function.
    • Best critical region of size alpha
    • Neyman-Pearson lemma
    • Likelihood ratio
    • UMP test (Uniformly Most Powerful test) of size alpha

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