Stat 517: Statistical Inference (Banner Course Number: 51700)

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Fall 2009 textbooks are:

For Cheng, G. -- James H Stapleton, Models for Probability and Statistical Inference, 2008 Edition, Recommended
For Cheng, G. -- Michael J Evans and Jeffrey S Rosenthal, Probability and Statistics: The Science of Uncertainty, 2004 Edition, Required


Spring 2010 textbook will be:

For Li, Bo -- Michael J Evans and Jeffrey S Rosenthal, Probability and Statistics: The Science of Uncertainty, 2004 Edition, Required

Outline:

  1. Distribution Theory
    1. Distribution functions and moment-generating functions
    2. Distributions associated with normal samples: c2, t, F
    3. Fundamental distribution theorem for normal samples


  2. Properties of Point Estimators
    1. Unbiasedness
    2. Mean squared error
    3. Consistency


  3. Methods of Constructing Point Estimators
    1. Method of moments
    2. Maximum likelihood
    3. Minimum variance unbiased
    4. Bayes


  4. Confidence Intervals

  5. Sufficient Statistics
    1. Factorization Theorem
    2. Regular exponential families


  6. Tests of Hypotheses
    1. Fundamentals: hypotheses, critical region, Type I and Type II errors, size and power
    2. Most powerful and uniformly most powerful tests
    3. Likelihood ratio tests