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is called the maximum-likelihood estimator (ML estimator).

Under the usual implicit assumption that all functions are sufficiently smooth,

$equation$

is a necessary condition.

The first example will be to find the ML estimator for the expectation value of a d-dimensional normal distribution. Let mk ∼ N(μ, Σ) with μ unknown but known Σ. It follows that

$equation$

Applying ...

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