Estimation theory - Wikiped.. - Estimation theory -...

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From Wikipedia, the free encyclopedia (Redirected from Statistical estimator) 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 1 of 8 02/03/2010 00:46
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not 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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Estimation theory - Wikiped.. - Estimation theory -...

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