Maximum-likelihood covariance estimator for centered Gaussian data ( $Σ$ )

For independent

Z_{i} \sim N_{p} (0, Σ)

with known zero mean,

Σ = \frac{1}{n} \sum_{i = 1}^{n} Z_{i} Z_{i}^{T} .

Table of contents
- Asymptotic covariance of the bivariate Gaussian covariance estimator Maximum-likelihood covariance estimator for centered Gaussian data

Asymptotic covariance of the bivariate Gaussian covariance estimator

a = Σ_{11}

,

c = Σ_{12}

, and

b = Σ_{22}

(Σ_{11}, Σ_{12}, Σ_{22})

has asymptotic covariance

2 a^{2} 2 a c 2 c^{2} 2 a c ab + c^{2} 2 b c 2 c^{2} 2 b c 2 b^{2} .

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Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 2 / 29K / b / Solution

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