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A note on minimum variance. (English) Zbl 0588.62039
Minimizing \(\int \{{\hat \theta}(x)\}^ 2f(x)d\mu\) is discussed under the unbiasedness condition: \(\int {\hat \theta}(x)f_ i(x)d\mu =c_ i\quad (i=1,...,p)\) and the condition (A): \(f_ i(x)\quad (i=1,...,p)\) are linearly independent, \[ \int \{f_ i(x)\}^ 2/f(x)d\mu <\infty \quad (i=1,...,k;\quad k\leq p),\quad and \]
\[ \int \{\sum^{p}_{i=1}a_ if_ i(x)\}^ 2/f(x)d\mu <\infty \quad implies\quad a_{k+1}=...=a_ p=0. \]

MSC:
62F10 Point estimation
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References:
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