The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves.

In an earlier paper (Rao, 1959), the author discussed the method of least squares when the observations are dependent and the dispersion matrix is unknown but an independent estimate is available. The unknown dispersion matrix was, however, considered as an arbitrary positive definite matrix. In the present paper we shall consider a class of problems where the dispersion matrix has a known structure and discuss the appropriate statistical methods. More specifically the structure of the dispersion matrix results from considering the parameters in the well-known Gauss-Markoff linear model as random variables. Let Y be a vector random variable with the structure