S551 & S552
Review of Topics
In S551, we covered:
• Basic topics such as
– Sample, population
– Random variable
– Parameter, Estimator, Estimate, Statistic
– Probability, Conditional probability, Bayes Thm
– Expectation, variance, moment generating
functions
• Discrete and continuous distributions
• Joint and conditional distributions
In S551, we covered:
• Distributions of new variables
– Transformations
– M.g.f. technique
• Sampling Distributions
• Limit theorems
In S552, we covered:
• Exponential families
• Point Estimation
– Maximum likelihood estimation
– Method of moments
– Least Squares Estimation
In S552, we covered:
• Some properties of estimators
– Unbiasedness
– Consistency
– Mean-square error consistency
– Sufficiency
– Completeness
In S552, we covered:
• Finding unbiased estimators with small
variance
– Rao-Blackwell Theorem: to find MVUE
– Lehmann-Scheffe Theorem: to find UMVUE
– Rao-Cramer inequality: to find a lower bound on
the variance  If an estimator is UE and has
variance=CRLB, then that estimator is UMVUE.
• Fisher information
In S552, we covered:
• Confidence intervals
– Pivotal quantities
– Approximate CIs by using CLT
• Hypothesis tests
– Concepts
– Neyman-Pearson lemma: to find MPT
– Monotone Likelihood Ratio: to find UMPT
– Likelihood ratio test
– Applications