There are two major types of estimators of random parameters: mean-squared (MS) and maximum a posteriori (MAP). The former does not use statistical information about the random parameters, whereas the latter does. MS estimators are the subject of this lesson; MAP estimators are the subject of Lesson 14.

The MSE is shown to equal a conditional expectation, i.e., . This result is referred to as the *fundamental theorem of estimation theory*. When θ and **Z**(*k*) are jointly Gaussian, then it is possible to compute this expectation, and, in fact, processes the data, **Z**(*k*), linearly. When θ ...

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