A note on minimum variance

Summary

Minimizing$\smallint \{ \hat \theta (x)\} ^2 f(x)d\mu$ is discussed under the unbiasedness condition:$\smallint \hat \theta (x)f_i (x)d\mu = c_i (i = 1,...p)$ and the condition (A):f _i (x) (i=1, ..., p) are linearly independent$\smallint \hat \theta (x)f_i (x)d\mu = c_i (i = 1,...p)$, and${{\{ \sum\limits_{i = 1}^p {a_i f_i (x)^2 } } \mathord{\left/ {\vphantom {{\{ \sum\limits_{i = 1}^p {a_i f_i (x)^2 } } {f(x)d\mu< \infty implies a_{k + 1} = ... = a_p = 0}}} \right. \kern-\nulldelimiterspace} {f(x)d\mu< \infty implies a_{k + 1} = ... = a_p = 0}}$.