Multivariate Analysis (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 7 - 8 of 8

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Question number: 7

» Multivariate Analysis » Principal Components » Correlations

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let

Equation

Determine

(i) The principal components y 1, y 2 and y 3.

(ii) The proportion of variance explained each one of them.

(iii) Correlation between the first principal components y 1 and the third original random variable.

Explanation

First find the eigen value and eigen vector pairs

Equation

Equation

Equation

To solve this equation, we get the eigen values is

Equation

Equation

The corresponding eigen vector for each eigen value is by using normalize the eigen vector by the equation

Equation

Equation

For λ 1 =6,

Equation

Equation

… (131 more words) …

Question number: 8

» Multivariate Analysis » Wishart's Distribution » Reproductive Properties

Appeared in Year: 2015

Essay Question▾

Describe in Detail

(i) Let A i be distributed as Wishart Equation , i = 1, 2 and A 1, A 2 be independent. Show that A 1 +A 2 is distributed as Equation .

(ii) If A is distributed as Equation , then CAC’ is distributed as Equation where C is a nonsingular matrix of order m.

Explanation

(i) We have Equation that is

Equation where Equation ) and Y i ’s are independent.

Similarly, Equation that is

Equation where Equation ) and Z i ’s are independent.

We know that A 1, A 2 are independent. So, Y i ’s are independent of Z i ’s

… (55 more words) …

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