Inferences in Growth Curve Models under Elliptical Settings

Abstract

The growth curve model Y with mean μ = Z1ΘZ'2 and covariance proportional to A U Σ is considered. Conditions are given under which a best linear unbiased estimator (blue) ?(Y) of μ and a best quadratic unbiased estimator (bque) exist. None of the matrices Z1, Z2, A and Σ are required to have full column rank. Explicit formulae for blue of L(μ) and for bque of Σ are obtained through there desired statistical properties rather than the least squares or maximum likelihood methods which is due to the fact that the probability density function of Y is not required to exist. The distributions of estimators are also studies so that the corresponding tests for the mean and the covariance are obtained. For illustration of our results, examples are also given in this talk.