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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 7 Large-sample Properties of Estimators*

*This lesson was written using many suggestions and inputs from Dr. Georgios B. Giannakis, Department of Electrical Engineering, University of Virginia, Charlottesville, VA.

Summary

Large-sample properties of an estimator mitigate the effect of the criterion function that is used to derive the estimator. The purpose of this lesson is to introduce four widely used large-sample properties of estimators, asymptotic unbiasedness, consistency, asymptotic normality, and asymptotic efficiency. The phrase large sample means an infinite number of measurements, although, in practice, estimators enjoy large-sample properties for much fewer than an infinite number of measurements.

Recall, from Lesson 6

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