## 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

**Illustrative reading:
**

*Mathematical Statistics and Data Analysis* -- by J. Rice

*Mathematical Statistics: A Text for Statisticians and Quantitative Scientists* -- by F. J. Samaniego

**GE3:**

SE, QL

**Potential Overlap:**

Similar topics are covered in STA 131B and 131C.

**History:**

None