SI&DA - Definition of 'Maximum Likelihood (ML) Estimators'

Definition of ‘Maximum Likelihood (ML) Estimators’

The maximum likelihood estimator searches for the max value of the pdf function $f_Y^{\theta }(y)$ where $\theta$ is our parameter to be estimated, we have said that $\theta$ is also equal to the mean of this pdf which is also equal to its max value, here’s way the ML Estimator.

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Theorem

If our observations $y_i$ are independent and identically distribuited then we can say:

$$\mathcal{L}(\theta |y)=\prod _i^{n}f(\theta |y_i)$$

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~Ex.:

For simplicity let’s say that our parameter $\Theta$ can take only 3 values:

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NOTE: The $T_{ML}$ is a consistent estimator

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