B.Tech Mathematics

 

MA 324      Statistical Inference and Multivariate Analysis       3-0-0-6

 

 

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.

 

Texts:

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

 

References:

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