LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

AC 43

M.Sc. DEGREE EXAMINATION – STATISTICS

THIRD SEMESTER – APRIL 2007

ST 3801/ 3805 / 3808 – MULTIVARIATE ANALYSIS

 

 

 

Date & Time: 24/04/2007 / 9:00 – 12:00      Dept. No.                                       Max. : 100 Marks

 

 

 

SECTION A

 

10 X 2 =20

 

ANSWER ALL QUESTIONS. EACH CARRIES TWO MARKS

 

 

1. Write the likelihood function corresponding to a sample of size drawn from .
2. Mention any two applications of F-distribution in Multivariate Statistical Analysis.
3. Find the distribution of if.
4. Mention any two properties of variance-covariance matrix.
5. How will you obtain the MLE of population correlation coefficient between two variables having bivariate normal distribution?
6. What do mean by agglomerative algorithms?
7. Define : Communalities
8. Define Non-central Chi-square statistic.
9. What is meant by “Expected Cost of Misclassification”?
10. Give an unbiased estimator of variance-covariance matrix in

 

 

SECTION B

 

5 X 8 = 40

 

ANSWER ANY FIVE. EACH CARRIES EIGHT MARKS

 

1. Derive the distribution of where and is a matrix of rank

 

1. State and prove a characterization of multivariate normal distribution

 

1. Obtain an expression of under usual notations.

 

1. Obtain the rule which minimizes Expected Cost of Misclassification(ECM) in the case of two multivariate normal populations assuming priori probabilities are known to be equal and the populations have equal variance-covariance matrices.
2. Show that where B,C,D and E are matrices of suitable order and mention any two places the above identity is used in multivariate analysis.

 

 

1. State and prove any two properties of Wishart’s Distribution.

 

1. Define Generalized variance. Show it is equal to the product of eigen roots of

 

 

1. Obtain expressions for the first r-principal components in a p-variate normal distribution.

 

SECTION C

 

2 X 20 = 40

 

ANSWER ANY TWO. EACH CARRIES TWENTY MARKS

 

1. Derive the conditional distribution of a sub vector of
2. Derive the sampling distribution sample correlation coefficient assuming the population multiple correlation coefficient is zero.

 

1. Derive the likelihood ratio test for assigned mean based on a sample of size N drawn from assuming is unknown.

 

1. Write short notes of the following :

• Similarity and Distance Measures.
• Discriminant Analysis
• Cluster Analysis
• Orthogonal Factor Model

 

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