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LOYOLA COLLEGE (AUTONOMOUS), CHENNAI 600 034
M.Sc.DEGREE EXAMINATION STATISTICS
THIRDSEMESTER APRIL 2018
16PST3MC01/ST3815 MULTIVARIATE ANALYSIS
Date: 24-04-2018 Dept. No. Max. 100 Marks
Time: 09:00-12:00
SECTION A
Answer ALL the questions (10 x 2 20)
1. Let X,Y and Z have trivariate normal distribution with null mean vector and Covariance matrix, find the distribution of X+Y.
2. Mention any two properties of multivariate normal distribution.
3. Write down the characteristic function of a multivariate normal distribution.
4. Explain use of the partial and multiple correlation coefficients.
5. Comment on repeated measurements design.
6. Describe Common factor and Communality.
7. Explain the classification problem into two classes.
8. Briefly explain K means method in clustering.
9. Outline the use of Discriminant analysis.
10. Write a short note on data mining.
PART- B
Answer anyFIVE questions (5X8=40 marks)
11. Find the multiple correlation coefficient between X1 and X2,X3,…,Xp . Prove that the
conditional variance of X1 given the rest of the variables cannot be greater than
unconditional variance of X1.
12. Derive the characteristic function of multivariate normal distribution.
13. Explain the procedure for testing the equality of dispersion matrices of multivariate normal
distributions.
14. Obtain the linear function to allocate an object to one of the two given normal populations.
18. Prove that the extraction of principal components from a dispersion matrix is the study of
characteristic roots and vectors of the same matrix.
PART- C
Answer anyTWO questions X 20 =40marks)
19. Derive the distribution function of the generalized T2 Statistic.
20. Define generalized variance.
Show that the sample generalized variance is zero if and if the rows of the
matrix of deviation are linearly dependent.
21. Outline single linkage and complete linkage clustering procedures with an
example.
If p X N then prove that Z DX N D p where D is qxp
matrix rank q≤p.
22. Let p N Y . Show that YY has distribution.
Prove that under some assumptions (to be stated), variance covariance
matrix can be written as in the factor analysis model. Also
discuss the effect of an orthogonal transformation.