Multivariate Analysis (ISS 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

Σ=(311131115)

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

ΣIλ=0

3λ1113λ1115λ=0

(3λ)[(3λ)(5λ)1… (525 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 Wmi(Ai Σ) , i = 1, 2 and A 1, A 2 be independent. Show that A 1 +A 2 is distributed as Wm1+m2(A1+A2 Σ) .

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

Explanation

(i) We have A1~Wm1(A1Σ) that is

A1=i=1m1YiYi where Yi~N(0,Σ) and Y i ’s are independent.

Similarly, A2~… (350 more words) …

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