Asymptotic normality refers to the property of a sequence of estimators whereby, as the sample size increases, the distribution of the estimator approaches a normal distribution. This concept is crucial in statistics as it allows for approximations of sampling distributions and facilitates the application of inferential methods, particularly in maximum likelihood estimation. The importance lies in the fact that even if the original data does not follow a normal distribution, the estimators can behave normally with a large enough sample size.
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