Concomitants and linear estimators in an i-dimensional extremal model

Abstract

We consider here a multivariate sample$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{X} _j = (\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{X} _{1 \cdot j} > ... > X_{i \cdot j} )$, 1≦j≦n, where the$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{X} _j$, 1≦j≦n, are independenti-dimensional extremal vectors with suitable unknown location and scale parameters λ and δ respectively. Being interested in linear estimation of these parameters, we consider the multivariate sample$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{Z} _j$, 1≦j≦n, of the order statistics of largest values and their concomitants, and the best linear unbiased estimators of λ and δ based on such multivariate sample. Computational problems associated to the evaluation ofμ ⁽ⁿ⁾ _i and Σ ⁽ⁿ⁾ _i , the mean value and the covariance matrix of standardized$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{Z} _j$, 1≦j≦n, are also discussed.