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A note on minimum variance

Authors:	K Takeuchi M Akahira

Institution:	(1) Faculty of Economics, University of Tokyo, Hongo, Bunkyo-ku, 113 Tokyo, Japan;(2) Statistical Laboratory, Department of Mathematics, University of Electro-Communications, Chofu, 182 Tokyo, Japan

Abstract:	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 ${{\{ \sum\limits_{i = 1}^p {a_i f_i (x)^2 } } \mathord{\left/ {\vphantom {{\{ \sum\limits_{i = 1}^p {a_i f_i (x)^2 } } {f(x)d\mu< \infty implies a_{k + 1} = ... = a_p = 0}}} \right. \kern-\nulldelimiterspace} {f(x)d\mu< \infty implies a_{k + 1} = ... = a_p = 0}}$ .

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