3 Hours/Week, 3 Credits

Distribution of quadratic forms: Distribution of general quadratic form, properties, expected values, moment and moment generating function, Cochrans’ thoerem. Multivariate normal distribution: Derivation of multivariate normal distribution, marginal, conditional, moments and moment generating functions. Properties of multivariate normal distribution. Tests of mean vector: Hotelling’s T2, Mahalanobish D2, Wishart distribution. Tests for covariance and correlation patterns and multivariate normality. Simulation of multivariate normal variate. Multivariate linear models: Multivariate linear regression, MANOVA, MANCOVA, covariance selection, conditional Gaussian distribution and conditional independence graph. Principal component analysis: Derivation of components, choosing principle components, properties, large sample inferences.