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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.

The conditions guarantying consistency and asymptotic normality of Least-Square estimators as well as the consistency of the usual tests for linear hypotheses in multivariate linear models are shown to be valid whenever almost optimal experimental designs are used.

Berry Esseen type bounds for the distribution of the nonlinear least-squares estimator as well as of a certain statistic useful for testing a hypothesis on a subset of the parameter vector are derived.

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.

In the linear model with tests for linear hypotheses on β are based on the normal distribution assumption. In this paper it is studied how much the distributions of the test-criterions differ from their distributions under normality when Yn is not normally distributed.

Usually the variance of independent observations resulting from a linear or a nonlinear relationship is estimated by the Least-Squares residual estimator. In this paper its asymptotic properties are investigated. Further the asymptotic behaviour of tests for one-sided hypotheses on the variance is studied. The paper splits into two parts, the first one concerned with linear and the second one with nonlinear models.

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.