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Lessons in Estimation Theory for Signal Processing, Communications, and Control, Second Edition by Jerry M. Mendel - Department of Electrical Engineering, University of Southern California, Los Angeles, California

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Lesson A Sufficient Statistics and Statistical Estimation of Parameters

Summary

The concept of sufficient statistic is an elegant tool in estimation, hypothesis testing, and decision theories. Sufficient statistic is a compaction of the information contained in the original data so that estimation using the sufficient statistic is as good as using the entire original data. The dimension of the sufficient statistic is much less than the original data and is also independent of it.

A formal definition of a sufficient statistic is given in this lesson; however, it is not very easy to use. The factorization theorem gives a direct method for the identification of a sufficient statistic from the likelihood of observations. A general structure is ...

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