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Topics for Multivariate Models

• Multivariate Data Analysis, Preliminary Data Analysis , Inhomogeneous Data , Missing Data, Outliers, Noisy Data, Time Alignment, Graphical Procedures, Dimensionality Reduction , Principal Component Analysis, Modelling techniques, Multiple linear regression, Principal component regression, Projection to Latent Structures, Multivariate Statistical Performance Monitoring
• Continuous and Batch Processes, random vectors and their distribution, linear transformations , Mahalanobis transformation, sample statistics and their properties, overall measures of dispersion in p-space, distances in p-space, simple graphical techniques, Cluster Analysis , hierarchical algorithms, dendrogram, Principal component analysis , definition and derivation of population PC's
• sample PC's, geometrical properties, The Multivariate Normal (MVN) distribution , conditional distributions, Wishart and Hotelling T-squared distributions, sampling distributions of the sample mean vector and covariance matrix, maximum likelihood estimation of the mean vector and covariance matrix, Hypothesis testing and confidence intervals , generalized likelihood ratio test, tests on the mean vector
• CI's for the components of the mean vector, Hypothesis testing and confidence intervals , tests on the difference between two mean vectors, testing equality of covariance matrices, CI's for the differences in the components of the mean vectors, Profile Analysis, Discriminant Analysis, Techniques for discrete multivariate data , discrete multivariate vectors, two-way contingency tables, sampling distributions, odds ratio, testing independence, correspondence analysis, higher order contingency tables, conditional independence, log-linear models.

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