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
Potential Overlap:
Similar topics are covered in STA 131B and 131C.
History:
None