Multivariate Analysis-Estimation (ISS (Statistical Services) 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 Equation , Equation

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

Explanation

Let

Equation

Equation

Given that Y and Z are independent, So

Equation

Equation

Equation

Equation

Equation

Equation

Equation

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.

Equation

from a bivariate normal distribution.

Explanation

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

Equation

Assume

Equation

So,

Equation

Equation

Equation

Equation

Equation

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