# STA 130B Mathematical Statistics: Brief Course

Units: 4

Format:
Lecture: 3 hours
Discussion: 1 hour

Catalog Description:
Transformed random variables, large sample properties of estimates. Basic ideas of hypotheses testing, likelihood ratio tests, goodness-of- fit tests. General linear model, least squares estimates, Gauss-Markov theorem. Analysis of variance, F-test. Regression and correlation, multiple regression.

Prerequisite: STA 130A or STA 131A or MAT 135A

Goals:
This course is a continuations of STA 130A.  It is designed to continue the integration of theory and applications, and to cover hypothesis testing, and several kinds of statistical methodology.

Summary of course contents:

• Probability/distributions theory results
• Transformation and the delta method
• Large sample distribution theory for MLE's and method of moments estimators
• Testing
• Basic ideas of hypotheses testing and significance levels
• The notion of a "best test"
• Likelihood ratio princible
• Testing hypotheses for means, proportions and variances
• Power and sample size
• Chi-square tests
• Goodness-of-fit tests
• Tests of independence and homogeneity (contingency tables)
• Linear Models
• The general linear model with and without normality
• Least squares estimation
• The Gauss-Markov Theorem
• Matrix Formulation
• Analysis of variance: one-way and randomized blocks
• Derivation and distribution theory for sums of square
• Analysis of variance table
• The F test as a likelihood ration test
• Concepts of randomization and blocking
• Regression and correlation
• Estimation and testing for simple linear regression
• Correlation and R^2
• Extensions to multiple regression
• Selected topics from the following
• Non-linear regression
• Log-linear models
• Bootstrapping
• Time series models

Restrictions:
None