Asymptotic property

Asymptotic property is a property of a parameter estimator that states its variability decreases as the sample size increases.

It is a fundamental concept in statistics that is used to assess the accuracy of an estimator.

How to calculate

  1. Calculate the bias and variance of the parameter estimator.

  2. As the sample size increases, the bias decreases while the variance remains constant.

  3. As the sample size increases, the variability of the estimator decreases.

  4. The estimator is said to be asymptotically unbiased if the bias is zero as the sample size increases.

  5. The estimator is said to have the asymptotic property if the variability of the estimator decreases as the sample size increases.

Examples

  1. Asymptotic property can be used to determine the accuracy of an estimator as the sample size increases.

  2. Asymptotic property can be used to assess the consistency of a parameter estimator across different samples.

  3. Asymptotic property can be used to determine the stability of the estimates when the underlying distribution changes.

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