STAT 512 -- EXAM 3 REVIEW SHEET 

I.  Estimation
  A.  Basic Ideas
     1. Definition of target parameter
     2. Point estimate and Interval estimate
     3. Estimate vs. Estimator
  B.  Judging Quality of Point Estimators
     1. Performance across repeated samples
     2. Accuracy vs. Precision
  C.  Bias and MSE of a Point Estimator
     1. Bias of an estimator
     2. Unbiased estimator
     3. MSE of an estimator
     4. MSE as a function of bias and variance of the estimator
     5. Comparing candidate estimators based on their MSE
  D.  Common Unbiased Estimators
     1. Y-bar as an estimator of mu
     2. Variance of Y-bar
     3. p-hat as an estimator of p
     4. Variance of p-hat
     5. (Y1-bar - Y2-bar) as an estimator of (mu1 - mu2)
     6. Variance of (Y1-bar - Y2-bar)
     7. (p1-hat - p2-hat) as an estimator of (p1 - p2)
     8. Variance of (p1-hat - p2-hat)
     9. Sample variance S^2 as an estimator of sigma^2
II.  Confidence Intervals
  A.  Properties of Interval Estimators
     1. Confidence Coefficient
     2. Two Sided Intervals, Lower Confidence Bounds, Upper Confidence Bounds
  B.  Pivotal Method
     1. Definition of Pivotal Quantity
     2. Using Distribution of Pivotal Quantity to set up a Probability Statement
     3. Solving Inequality for Parameter to get CI formula
  C.  Large-Sample Confidence Intervals
     1. General Formula for CIs when unbiased estimator has approximately normal sampling distn
     2. Meaning of confidence level
     3. Examples of Large-sample CIs
       a. CI for mu
       b. CI for p
       c. CI for mu1 - mu2
       d. CI for p1 - p2
     4. Interpreting CIs in the context of the variable(s) in the problem
  D.  Sample Size Determination Formulas
  E.  Small-sample CIs for mu and for mu1 - mu2
     1. Role of the t-distribution
     2. One-sample and Two-sample situations with small sample sizes
     3. Robustness of t-based CI procedures
  F.  CIs for variances
     1. Chi-square-based CI for one variance
     2. F-based CI for ratio of two variances
III. Brief Introduction to Hypothesis Testing
  A.  Null Hypothesis and Alternative (research) Hypothesis
  B.  Type I and Type II errors in Hypothesis Testing 
     1. Rejection Region
     2. Significance Level alpha
  C.  Relationship between Hypothesis Testing and CIs
     1. Connection Between Two-sided Tests and Two-Sided CIs
     2. Connection Between One-sided Tests and Lower (or Upper) Confidence Bounds
IV. Properties of Point Estimators
  A.  Unbiasedness and Small Variance
  B.  Relative efficiency
     1. Why is it used?
     2. Calculating relative efficiency of one estimator compared to another
  C.  Cramer-Rao Lower Bound
     1. Calculating CRLB
     2. Definition of Efficient estimator
  D.  Sufficiency
     1. Definition of sufficient statistic
     2. What sufficiency intuitively means
     3. Likelihood Function
     4. Factorization theorem and how it is used
     5. One-to-one function of a sufficient statistic
  E.  Minimum Variance Unbiased Estimation
     1. Rao-Blackwell Theorem
     2. Minimal sufficient statistic
     3. Complete sufficient statistic
     4. Lehman-Scheffe Theorem and its usefulness
     5. One-parameter Exponential Family
     6. Finding a complete sufficient statistic when pdf in exponential family
     7. Finding MVUE for a parameter, based on the complete sufficient statistic
     8. Finding MVUE for a function of a parameter, based on the complete sufficient statistic