Large Sample Properties

It often happens that an estimator does not satisfy one or more of the desirable statistical properties in small samples. But as the sample size increases indefinitely, the estimator possesses several desirable statistical properties. These properties are known as the large-sample, or asymptotic, properties.

Asymptotic Unbiasedness. An estimator 0 is said to be an asymptotically unbiased estimator of 0 if lim E(0n) = 0

where 0n means that the estimator is based on a sample size of n and where lim means limit and n ^to means that n increases indefinitely. In words, 0 is an asymptotically unbiased estimator of 0 if its expected, or mean, value approaches the true value as the sample size gets larger and larger. As an example, consider the following measure of the sample variance of a random variable X:

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