This course is designed to provide fundamental concepts of multivariate distribution. Student gathers knowledge to identify the differences among multivariate sampling distribution, multivariate central and non-central distribution.

Understand the theoretical and application based concepts of multivariate sampling distribution.

Calculate mean vector, variance-covariance matrix for different multivariate distributions and perform inferential statistics.

Understand multivariate normal distribution, maximum likelihood estimation, Wishart’s distribution, Hotelling’s T2 distribution;

Parameter estimation procedure and Hypothesis Testing for multivariate data.

After completing this course, students will be able to

conceptualize the basic idea of multivariate central and non-central distribution.

explore and summarize multivariate sampling distribution

synthesize the statistical knowledge and techniques required in multivariate sampling distribution.

real life application of multivariate central and non-central distribution.

Multivariate Normal Distribution: Introduction, Marginal and conditional distributions, Moments, moment generating function and properties of multivariate normal distribution, Maximum likelihood estimation of mean vector and covariance matrix of multivariate normal distribution and their properties.

Distribution of Quadratic Form: Introduction, Non-central c2, t and F distributions, Distribution of general quadratic forms, Expected values, Moments and moment generating functions, Properties of quadratic forms.

Multivariate Sampling Distribution: Introduction, Derivation and distribution of Hotelling’s T2 – statistic, properties and applications, Distribution of sample covariance matrix and sample generalized variance, Wishart distribution and its properties, Distribution of latent roots of a dispersion matrix, Multivariate t- distribution and its properties, Test for a mean vector, Test for equality of mean vectors.

Mixture of Multivariate Distributions: Introduction, Mixture of multivariate normal distributions and its properties, Mixture of multivariate t-distributions and its properties.

1)

Hair, J. F., R. L. Tatham, R. E., Anderson & W. Black (2006). Multivariate data analysis. Upper Saddle River, NJ: Pearson Prentice Hall.

2)

Härdle, W. K., & L. Simar (2012). Applied multivariate statistical analysis. Springer.

3)

Anderson,T.W. (2003). An Introduction to Multivariate Statistical Analysis,  5th ed., Wiley, N.Y.

4)

Johnson, R. A.  and D. W Wichern (2002). Applied Multivariate Statistical Analysis, 5th ed., Prentice Hall, N.Y.

5)

Nachtsheim, C. J., J., Neter & W. Li (2005). Applied linear statistical models.

6)

Richard, A. J., & W. W. Dean (2002). Applied multivariate statistical analysis. Prentice Hall, New York.