an:00064366
Zbl 0764.62055
Wimmer, Gejza
Linear model with variances depending on the mean value
EN
Math. Slovaca 42, No. 2, 223-238 (1992).
00007414
1992
j
62J05 62H12
uniformly best linear unbiased estimators; locally best linear unbiased estimator
Let \((Y,X\beta,\Sigma)\) be a linear regression model. The result of the observations is a realization of a random vector \(Y_{n,1}\), whose mean value is \(E_ \beta Y=X\beta\), \(X_{n,k}\) is a known design matrix, \(\beta_{k,1}\in R^ k\) the vector of unknown parameters, the covariance matrix of the vector \(Y\) depends on \(\beta\),
\[
\Sigma=\sigma^ 2\Sigma(\beta)=\text{diag}(\sigma^ 2(a+b| e_ i' X\beta|^ 2))_{1\leq i\leq n},
\]
where \(\sigma^ 2\), \(a\) and \(b\) are known positive constants, and \(e_ i'\) is the transpose of the \(i\)th unity vector.
The \(\beta_ 0\)-locally best linear unbiased estimator of a linear function of the parameter \(\beta\) is obtained.
N.Leonenko (Kiev)