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local asymptotic normality : ウィキペディア英語版
local asymptotic normality
In statistics, local asymptotic normality is a property of a sequence of statistical models, which allows this sequence to be asymptotically approximated by a normal location model, after a rescaling of the parameter. An important example when the local asymptotic normality holds is in the case of iid sampling from a regular parametric model.
The notion of local asymptotic normality was introduced by .
== Definition ==

A sequence of parametric statistical models } is said to be locally asymptotically normal (LAN) at ''θ'' if there exist matrices ''rn'' and ''Iθ'' and a random vector such that, for every converging sequence ,
:
\ln \frac} - \frac12 h'I_\theta\,h + o_h_n}}\ \ \mathcal\Big( h'I_\theta\,h,\ h'I_\theta\,h\Big).

The sequences of distributions P_ and P_ are contiguous.〔

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