MA 324: Statistical Inference and Multivariate Analysis

Course Syllabus

  • Review of different transformation techniques, modes of convergence, law of large numbers, and central limit theorem; Sampling distributions based on normal distributions, multivariate normal distribution.

  • Point estimation: sufficiency, Neymann-Fisher factorization theorem, unbiased estimation, method of moments, maximum likelihood estimation, consistency and asymptotic normality of maximum likelihood estimator.

  • Interval estimation: confidence coefficient and confident level, pivotal method, asymptotic confidence interval, Bootstrap confidence interval.

  • Hypothesis testing: type-I and type-II errors, power function, size and level, test function and randomized test, most powerful test and Neyman-Pearson lemma, likelihood ratio test, p-value

  • Multiple linear regression: least squares estimation, estimation of variance, tests of significance, interval estimation, multicollinearity, residual analysis, PRESS statistic, detection and treatment of outliers, lack of fit.

  • Multivariate analysis: principle component analysis, factor analysis, canonical correlations, cluster analysis.

Text Books

  • D. C. Montgomery, E. A. Peck and G. G. Vining, Introduction to Linear Regression Analysis, 5th Ed., Wiley, 2012.
  • R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis, 6th Ed., Prentice Hall of India, 2012.

Reference Books

  • N. R. Draper and H. Smith, Applied Regression Analysis, 3rd Ed., Wiley, 2000.
  • S. Weisberg, Applied Linear Regression, 1st Ed., Wiley, 2005.
  • T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 3rd Ed., Wiley, 2012.
  • W. K. Härdle and L. Simar, Applied Multivariate Statistical Analysis, 3rd Ed., Springer, 2012.

Evaluation

Weights in different examinations are as follows:

  • Quiz III: 15 marks (April 09 April 08 during class)
  • End-semester examination: 30 marks (May 08 from 2 pm to 5 pm)

For each examination, linear scaling will be used (if needed).
Letter grade based on your performance in 5 exams (3 quizzes, MS, ES) following a relative grading scheme

Course Materials

Lecture Slides

Problem Sets