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An extension of a central limit theorem of F. EICKER for linear vector forms is used to derive conditions for the asymptotic normality of Least-Square Estimators in multivariate linear singular models with stochastically independent error terms. These conditions are shown to be necessary too in some cases. Several previous results concerning asymptotic normality of Least-Square Estimators in regular models are special cases of the theory developed in this paper.

This paper deals with asymptotic properties of the Least-Square Estimator and of two-stage estimators in multiariate linear models where the case of singular experimental matrices is included. Fristly we prove the asymptotic optimality of the best linear unbiased estimator (BLUE) when the convariance matrix is assumed to be known in a partial class of linear asymptotically unbiased and consistent sequences of estimators. Comparison of two sequences is made by the help of limits of covariance matrices. Secondly conditions are given under which sequence of Blue's. Furthermore there are a lot of cases in which the ineffienent ordinary Least-Square Estimator (OLSE) becomes asymptotically an efficient estimator when the sample size increases. General conditions are obtained under which this fact holds. Certain examples are discussed for illustration.

The general nonlinear regression model is considered, where the error distribution can be nonnormal. In this paper we present tests, confidence intervals and estimators for both the regression coefficients and the variance of the observations which perform well in the sense of second order asymptotic theory. In particular, robustness results for deviations from the normal distribution are given including distributions with either known or unknown skewness and kurtosis.