STAT 512 -- POST-EXAM 3 REVIEW SHEET 

** NOTE:  The final exam will contain questions from throughout the semester.
** Also study the material on the first 3 review sheets!!!

I.  Method of Moments
  A.  Population Moments and Sample Moments
  B.  Setting up equation(s) to estimate parameter(s)
  C.  Solving equation(s) for parameter(s)
  D.  A typical weakness of MMEs
II. Method of Maximum Likelihood
  A.  Writing out the likelihood function based on a sample of data Y1,...,Yn
  B.  Maximization of the (log) likelihood by taking its derivative with respect to target parameter
  C.  Setting derivative to zero and solving for target parameter
  D.  Checking second-derivative condition to ensure maximum was found
  E.  Finding MLEs of two (or several) parameters simultaneously
  F.  Relationship of MLEs to sufficient statistics
  G.  Invariance Property of MLEs and how it is useful
III. Asymptotic (Large-sample) Properties of Point Estimators
  A.  Consistency
     1. Formal Definition of Consistency
     2. Theorem relating consistency to unbiasedness and asymptotic variance
  B.  Convergence in Probability 
     1. Using the helpful 4-part theorem about convergence in probability
  C.  Examples of Consistent Estimators
     1. Law of Large Numbers (about the sample mean)
     2. Consistency of the sample variance
  D.  Slutsky's Theorem
     1. How does it validate many of our large-sample inferences?
     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.  Large-Sample properties of MLEs
     1. Large-sample distribution of any MLE (assuming regularity conditions)
     2. Formula for the large-sample variance of an MLE
     3. "Consistent, asymptotically normal, asymptotically efficient" property
     4. Large-sample CI formula based on any MLE
  F.  Delta Method
     1. Large-sample distribution of a FUNCTION of an MLE
     2. Formula for the large-sample variance of a FUNCTION of an MLE
     3. Large-sample CI formula for a FUNCTION of our parameter, based on an MLE