Likelihood of unbiased estimator of covariance matrix

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Given that $\boldsymbol{S}$ is the unbiased estimator of the covariance population matrix $\boldsymbol{\Sigma_0}$, $\hat{\boldsymbol{\gamma}}$ is the estimator of $\boldsymbol{\gamma_0}$ which minimises: $F(\boldsymbol{S},\boldsymbol{\Sigma}(\boldsymbol{\gamma}))$

where $\hat{\boldsymbol{\gamma}}$ minimises $(vech(\boldsymbol{S}-\boldsymbol{\Sigma}(\boldsymbol{\gamma})))^T\boldsymbol{U}^{-1}(vech(\boldsymbol{S}-\boldsymbol{\Sigma}(\boldsymbol{\gamma})))$ where $\boldsymbol{U}$ is symmetric and positive definite.

What is the likelihood of $vech{\boldsymbol{S}}$?