SELECTION SCHEMES - FROM THE GENEALOGICAL REPRESENTATION TO THE STATISTICAL-MODEL - ASYMPTOTIC VALIDITY

The aim of this paper is to give a proof of the asymptotic validity of the model described by Mangin and Vincourt (1992). This proof general izes the kind of proof that can be found in the bibliography for parti cular models. To help the reader with the notation and demonstrations, all topics included in this paper am first described in the framework of an example, and then generalized. We begin with the study of the f ixed effect model generated by the rules given by Mangin and Vincourt (1992) and we include the additional conditions which maintain the ran k of the estimate parameter space. We give the properties of the rando m variable used to sample in each population, and the exact structure of the random effects. Finally, we show that the rules given by Mangin and Vincourt (1992), which give the variances and covariances of the various levels of the random effects, am correct for a given dimension or asymptotically.