Statistical Inference and Multivariate Analysis

Code: MA3151 | L-T-P-C: 3-0-0-6

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.

Texts:

• R. V. Hogg, J. W. McKean and A. T. Craig, Introduction to Mathematical Statistics, Eighth Edition, Pearson, 2020.
• D. C. Montgomery, E. A. Peck and G. G. Vining, Introduction to Linear Regression Analysis, Sixth Edition, Wiley, 2021.
• R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis, Sixth Edition, Prentice Hall of India, 2015.

 

References:

• V. K. Rohatgi and A. K. Saleh, An Introduction to Probability and Statistics, Third Edition, Wiley, 2015.
• G. Casella and R. L. Berger, Statistical Inference, Second Edition, Cengage Learning, 2006
• N. R. Draper and H. Smith, Applied Regression Analysis, Third Edition, Wiley, 2000.
• S. Weisberg, Applied Linear Regression, First Edition, Wiley, 2005.
• T. W. Anderson, An Introduction to Multivariate Statistical Analysis, Third Edition, Wiley, 2012.
• W. K. Härdle and L. Simar, Applied Multivariate Statistical Analysis, Fifth Edition, Springer, 2019.