Restriction and Selection in Multinormal Distributions

Abstract

Maximum likelihood estimators of the parameters of a $p$-dimensional multinormal population are derived in this paper which are applicable when sample selection and observation is restricted with respect to $x_1$ but otherwise unrestricted with respect to $x_2, \cdots, x_p$. Restrictions imposed may consist of truncation, censoring, or a selection which results in full observation of all sample specimens with respect to $x_1$, but eliminates certain sample specimens from subsequent observation with respect to $x_2, \cdots, x_p$.