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  "body": "\n## Summary\n\nA sequence of statistical models is locally asymptotically normal (LAN) at a parameter value if its log-likelihood ratios have a special form at scale $1/\\sqrt{n}$.\nAt that scale they look like those of a single observation from a normal location model.\nThe notion is due to Lucien Le Cam.\nSmooth i.i.d. parametric models are LAN, with the Fisher information as the covariance.\nLAN is the setting of the asymptotic optimality theory of estimators and tests: the convolution theorem and the local asymptotic minimax theorem.\n\n## Explanations\n\n### L1 human\n\nWith $n$ observations, parameter values that differ by much more than $1/\\sqrt{n}$ are easy to tell apart, and values that differ by much less are impossible to tell apart.\nThe interesting scale is exactly $1/\\sqrt{n}$.\nLAN says that at this scale, every smooth model behaves like the simplest model there is: one normal observation whose mean is the unknown local parameter.\nSo asymptotic questions about complicated models reduce to easy questions about the normal distribution.\n",
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