Statistical Inference and Multivariate Analysis

Code: MA324 | L-T-P-C: 3-0-0-6

Prerequisites: MA225 or Equivalent

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 analysis6

Texts:

1. R. V. Hogg, J. W. McKean and A. T. Craig, Introduction to Mathematical Statistics, 7th Ed., Pearson, 2013.
2. D. C. Montgomery, E. A. Peck and G. G. Vining, Introduction to Linear Regression Analysis, 5th Ed., Wiley, 2012.
3. R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis, 6th Ed., Prentice Hall of India, 2012.

References:

1. V. K. Rohatgi and A. K. Saleh, An Introduction to Probability and Statistics, 3rd Ed., Wiley, 2015.
2. G. Casella and R. L. Berger, Statistical Inference, 2nd Ed., Cengage Learning, 2006.
3. N. R. Draper and H. Smith, Applied Regression Analysis, 3rd Ed., Wiley, 2000.
4. S. Weisberg, Applied Linear Regression, 1st Ed., Wiley, 2005.
5. T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 3rd Ed., Wiley, 2012.
6. W. K. Härdle and L. Simar, Applied Multivariate Statistical Analysis, 3rd Ed., Springer, 2012.