Sufficient Estimators and Sufficient Statistics

An estimator $\hat{\theta}$ is sufficient if it makes so much use of the information in the sample that no other estimator could extract from the sample, additional information about the population parameter being estimated. The sample mean $\overline{X}$ utilizes all the values included in the …

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Consistent Estimator (2014)

Statistics is a consistent estimator of a population parameter if “as the sample size increases, it becomes almost certain that the value of the statistics comes close (closer) to the value of the population parameter”. If an estimator (statistic) is considered consistent, it becomes more …

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Unbiasedness of the Estimator (2013)

The unbiasedness of the estimator is probably the most important property that a good estimator should possess. In statistics, the bias (or bias function) of an estimator is the difference between this estimator’s expected value and the true value of the parameter being estimated. An …

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