WEBVTT
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We have seen so far two ways of
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estimating an unknown parameter.
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We can use the maximum a
posteriori probability
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estimate, or we can use the
conditional expectation.
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That is, the mean of the
posterior distribution.
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These were, in some sense,
arbitrary choices.
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How about imposing a performance
criterion, and
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then finding an estimate which
is optimal with respect to
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that criterion?
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This is what we will be
doing in this lecture.
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We introduce a specific
performance criterion, the
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expected value of the squared
estimation error, and we look
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for an estimator that is optimal
under this criterion.
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It turns out that the optimal
estimator is the conditional
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expectation.
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And this is why we have been
calling it the least mean
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squares estimator.
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It plays a central role because
it is a canonical way
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of estimating unknown
random variables.
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We will study some of its
theoretical properties, and we
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will also illustrate its use and
the associated performance
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analysis in the context
of an example.