Search

In this paper a method is developed for estimating the parameters in the multivariate normal distribution in which the missing observations are not restricted to follow certain patterns as in most previous papers. The large sample properties of the estimators are discussed. Equivalence with maximum likelihood estimators has been established for a subclass of problems. The results of some simulation studies are provided to support the theoretical development. [ABSTRACT FROM AUTHOR]

It is claimed that the reasons for using matrices of derivatives, in appropriate situations, are as compelling as those for using matrices. This paper provides basic material for such use. Different types of matrix derivatives are defined and illustrated. Simple and easy techniques are then derived and are shown to be applicable to a considerable collection of matrix functions. Applications are made to such problems as establishing matrix integrals from scalar ones, determining maximum likelihood estimates for complex likelihood functions, optimizing matrix functions when there are matrices of side conditions, and evaluating the Jacobians of certain classes of transformations. The emphasis is on simplicity of derivation and on breadth of application. [ABSTRACT FROM AUTHOR]

In this paper we review the literature on the problem of handling multivariate data with observations missing on some or all of the variables under study. We examine the ways that statisticians have devised to estimate means, variances, correlations and linear regression functions from such data and refer to specific computer programs for carrying out the estimation. We show how the estimation problems can be simplified if the missing data follows certain patterns. Finally, we outline the statistical properties of the various estimators. [ABSTRACT FROM AUTHOR]

Negative components of variance estimates may arise when the usual specification of statistically independent random variables is false. A class of such situations is considered here, viz., those in which the assumption of sampling from infinite populations is incorrect. [ABSTRACT FROM AUTHOR]

Simple consistent estimates are derived for the parameters of a multivariate exponential distribution. The mean squared error of the estimates is computed, and a lower bound for their efficiency is derived. A precise lower bound for the efficiency is computed in the bivariate case. It does not seem feasible to compute the efficiency precisely in the multivariate case. Some attention is given to the behavior of the estimates when observations are rounded prior to analysis. [ABSTRACT FROM AUTHOR]