DEPARTMENT OF STATIS TICS
COLLEGE OF ARTS & SCIENCES, ROOM 118
330.972.6886 (TELEPHONE)
Course Description
3470:652
Prerequisite:
Advanced Mathematical Statistics
3 credits
3470:651 Probability and Statistics.
Course Description: Convergence of random variables; the Central Limit Theorem;
theory of estimation; theory of hypothesis testing; the multivariate normal density;
introduction to linear models; Bayesian statistics.
Course Topics:
Sampling and Statistics
Random Samples: Statistics, Unbiasedness
Confidence Intervals
Random Interval: Confidence Coefficient, Pivot
Normal Confidence Intervals: Mean, Proportions, Differences in Means and
Proportions
Quartiles: Confidence Limits, Tolerance Limits
Introduction to Hypothesis Testing
Basics: Hypotheses, Critical Region, Type I and Type II Errors, Chi-Square Tests
Maximum Likelihood Methods
Likelihood Function: Estimation
Variance Considerations: Rao-Cramer Lower Bound
Hypothesis Testing: Newman Pearson, UMP Tests, Likelihood Ratio
Properties of Estimators
Point Estimators: Sufficiency, Completeness, MVUE
Other Theory: Exponential Classes, Functions of Parameters
Bayesian Statistics
Basics: Prior and Posterior Distributions, Risk
Inference: Bayes Estimator, Bayes Intervals
Optional Topics
Sequential Statistics: Estimation, SPRT
Nonparametric Statistics: Liner Rank Statistics, Applications
Fall 2014