STA 130B Mathematical Statistics: Brief Course

Units: 4

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

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


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.