基本介紹
- 中文名:漸近正態估計
- 外文名:asymptotically normal estimate
- 簡稱:CAN估計
- 所屬學科:數學(統計學)
- 別名:相合漸近正態估計
- 舉例:樣本均值,樣本矩等
基本介紹,相關概念與定理,例題解析,
基本介紹
定義 設
是
的估計量,如果存在一串
,滿足
,其中
,使得當
時,有
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則稱
是
的漸近正態估計,
稱為
的漸近方差。
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當樣本容量n足夠大時,對於一個漸近正態估計
,可以用
作為
的近似分布,從而可以對
進行區間估計。
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對某個待估參數
,如果存在著漸近正態估計,這樣的估計可能並不唯一。因此漸近方差的大小就可以作為比較這些估計優劣的一個準則。
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相關概念與定理
最優漸近正態估計設
為待估參數
的一個漸近正態估計,漸近方差為
,若對
的任意漸近正態估計
,漸近方差記內
、有
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定理 漸近正態估計一定是相合估計。
證明: 設
是
的漸近正態估計,由定義,對任意
及k>0,當n充分大時
必須充分小,因此
,故當
時有
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例題解析
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故
是p的漸近正態估計,漸近方差為
。
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