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Estimation theory
is a branch of statistics and signal processing that deals with estimating the values of
parameters based on measured/empirical data. The parameters describe an underlying physical setting in such
a way that the value of the parameters affects the distribution of the measured data. An estimator attempts to
approximate the unknown parameters using the measurements.
For example, it is desired to estimate the proportion of a population of voters who will vote for a particular
candidate. That proportion is the unobservable parameter; the estimate is based on a small random sample of
voters.
Or, for example, in radar the goal is to estimate the location of objects (airplanes, boats, etc.) by analyzing the
received echo and a possible question to be posed is "where are the airplanes?" To answer where the
airplanes are, it is necessary to estimate the distance the airplanes are at from the radar station, which can
provide an absolute location if the absolute location of the radar station is known.
In estimation theory, it is assumed that the desired information is embedded in a noisy signal. Noise adds
uncertainty, without which the problem would be deterministic and estimation would not be needed.
1 Estimation process
2 Basics
3 Estimators
4 Examples
4.1 Unknown constant in additive white Gaussian noise
4.1.1 Maximum likelihood
4.1.2 Cramér–Rao lower bound
4.2 Maximum of a uniform distribution
5 Applications
6 See also
7 Notes
8 References
9 Reference list
The entire purpose of estimation theory is to arrive at an estimator, and preferably an implementable one that
could actually be used. The estimator takes the measured data as input and produces an estimate of the
parameters.
It is also preferable to derive an estimator that exhibits optimality. Estimator optimality usually refers to
achieving minimum average error over some class of estimators, for example, a minimum variance unbiased
estimator. In this case, the class is the set of unbiased estimators, and the average error measure is variance
(average squared error between the value of the estimate and the parameter). However, optimal estimators do
Estimation theory  Wikipedia, the free encyclopedia
http://en.wikipedia.org/wiki/Statistical_estimator
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View Full Documentnot always exist.
These are the general steps to arrive at an estimator:
In order to arrive at a desired estimator for estimating a single or multiple parameters, it is first
necessary to determine a model for the system. This model should incorporate the process being
modeled as well as points of uncertainty and noise. The model describes the physical scenario in which
the parameters apply.
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 Spring '10
 eamir

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