Multivariate Analysis-Estimation (ISS Statistics Paper II (Old Subjective Pattern)): Questions 1 - 2 of 2

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Question number: 1

» Multivariate Analysis » Estimation » Covariance Matrix

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Let X~N3(0,Σ) , Σ=(1ρ0ρ1ρ0ρ1)

Find ρ such that X 1 +X 2 +X 3 and X 1 -X 2 -X 3 are independent.

Explanation

Let

Y=X1+X2+X3=(111)(X1X2X3)=AX

Z=X1X2X3=(111)(X1X… (101 more words) …

Question number: 2

» Multivariate Analysis » Estimation » Covariance Matrix

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Find the maximum likelihood estimator of the 2×1 mean vector µ and the 2×2 covariance matrix ∑ based on the random sample.

X=[34546477]

from a bivariate normal distribution.

Explanation

We known that the maximum likelihood estimator of multivariate normal distribution is

μ=X_andΣ=i=1n(X_iX_)(X_iX_)n

Assume

X_… (206 more words) …

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