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- W1988424095 abstract "Suppose there are $n$ normal populations $N(mu_i, 1), i = 1, cdots, n$ and that one random observation from each of these $n$ populations is given. Let $x_1 leqq x_2 leqq cdots leqq x_n$ be the observations when arranged in order of magnitude and let the corresponding $n$ random variables be denoted by $X_i, i = 1, cdots, n.$ The following theorem is proved: THEOREM. begin{equation*}operatorname{Var}big(sum^n_{i = 1} c_i X_ibig), text{where}end{equation*}begin{equation*}tag{1}sum^n_{i = 1} c_i = 1,end{equation*} is minimum when $c_i = 1/n, i = 1, cdots, n.$ The above theorem may be applied to provide a direct proof of the result that $sum^n_{i = 1}X_i$ is the best unbiased linear function of order statistics for estimating the sum $sum^n_{i = 1}mu_i.$" @default.
- W1988424095 created "2016-06-24" @default.
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- W1988424095 date "1956-09-01" @default.
- W1988424095 modified "2023-09-27" @default.
- W1988424095 title "On Minimum Variance Among Certain Linear Functions of Order Statistics" @default.
- W1988424095 doi "https://doi.org/10.1214/aoms/1177728196" @default.
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