Linear sufficiency and some applications in multilinear estimation

In the linear model Y = X[beta] + u the question arises when a linear transformation z = Ly contains all information of the linear model. This problem was solved by[2], Drygas (, forthcoming) and [11]). As an application the estimation of the variance of the observations, its skewness, and its kurtosis are considered. This is done by considering so-called derived models. ( [1], Fourth Berkeley Symp. Math. Statist. Prob. 1, 1-36; [14], Metrika 27, 103-113;[10], Math. Operationsforsch. Statist. Ser. Statist. 9, 443-478). Linear sufficient statistics are derived for these problems.