Geodesic
Locally and uniformly best estimators in replicated regression model
Applications of Mathematics, Tome 28 (1983) no. 5, pp. 386-390.

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The aim of the paper is to estimate a function $\gamma=tr(D\beta\beta')+tr(C\sum)$ (with $d, C$ known matrices) in a regression model $(Y, X\beta,\sum)$ with an unknown parameter $\beta$ and covariance matrix $\sum$. Stochastically independent replications $Y_1,\ldots, Y_m$ of the stochastic vector $Y$ are considered, where the estimators of $X\beta$ and $\sum$ are $\bar{Y}=\frac 1 m \sum ^m _{i=1} Y_i$ and $\hat{\sum}=(m-1)^{-1} \sum^m_{i=1}(Y_i-\bar{Y})(Y_i-\bar{Y})'$, respectively. Locally and uniformly best inbiased estimators of the function $\gamma$, based on $\bar{Y}$ and $\hat{\sum}$, are given.
DOI : 10.21136/AM.1983.104049
Classification : 62H12, 62J05
Keywords: replicated regression model; best unbiased estimators 
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     title = {Locally and uniformly best estimators in replicated regression model},
     journal = {Applications of Mathematics},
     pages = {386--390},
     publisher = {mathdoc},
     volume = {28},
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Volaufová, Júlia; Kubáček, Lubomír. Locally and uniformly best estimators in replicated regression model. Applications of Mathematics, Tome 28 (1983) no. 5, pp. 386-390. doi : 10.21136/AM.1983.104049. http://geodesic.mathdoc.fr/articles/10.21136/AM.1983.104049/

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