Syllabus
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Course Code: ST-401 Course Name: Multivariate Analysis |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Notion of multivariate distribution, multivariate normal distribution of linear combination of normal variates, Marginal and Conditional distributions, Multiple and partial correlation coefficients. Characteristic function of a random vector, characteristic function when the random vector is normally distributed. Moments and semi-invariants of multivariate normal distribution.Estimation of the mean vector and covariance matrix, maximum likelihood estimator of the parameters of multivariate normal distribution. |
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| 2 | The distribution of the sample mean vector and sample dispersion matrix. Sample correlation coefficient, maximum likelihood estimators of total, partial and multiple correlation coefficients; sampling distribution of simple, partial and multiple correlation coefficients when the corresponding population correlation coefficients are zero.Testing hypotheses of significance of these distributions. |
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| 3 | Hotteling’s T2 and Mahalanobis D2-Statistic; Justification , distribution and uses . The multivariate Behren’s Fisher Problem and its solution. Classification Problem : Standards of good classification, Baye’s and minimax regions for classification into one of two known multivariate normal populations when the parameters are known and unknown. Fisher’s linear discriminator, Anderson’sdiscriminator. |
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| 4 | WishartDistribution : Definition, Characteristic function and properties. Sample generalized variance, asymptotic distribution of sample generalized variances. Principal components in the population, Canonical correlation in the population. |
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