# 充分统计量

## 費雪分解定理

${\displaystyle f_{\theta }(x)=h(x)g_{\theta }(T(x)).}$

## 最小充分统计量

1. S(X)是充分统计量，
2. 如果T(X)是一个充分统计量，那么存在一个函数f 使得 S(X)= f(T(X))。

${\displaystyle {\frac {f_{\theta }(x)}{f_{\theta }(y)}}}$θ无关${\displaystyle \Leftrightarrow }$ S(x)= S(y).

## 註釋

1. ^ Fisher, R.A. On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society A. 1922, 222: 309–368 [2017-12-25]. JFM 48.1280.02. JSTOR 91208. doi:10.1098/rsta.1922.0009. （原始内容存档于2017-07-29）.
2. ^ Dodge (2003) — entry for minimal sufficient statistics
3. ^ Lehmann and Casella (1998), Theory of Point Estimation, 2nd Edition, Springer, p 37
4. ^ Lehmann and Casella (1998), Theory of Point Estimation, 2nd Edition, Springer, page 42

## 参考文献

• Kholevo, A.S., Sufficient statistic, Hazewinkel, Michiel (编), 数学百科全书, Springer, 2001, ISBN 978-1-55608-010-4
• Lehmann, E. L.; Casella, G. Theory of Point Estimation 2nd. Springer. 1998. Chapter 4. ISBN 0-387-98502-6.
• Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9