Estimation of Parameters from Incomplete Multivariate Samples

Abstract The problem considered is that of using all of the observations in a sample of multivariate observations when for some of the observations values for certain of the characters are missing. This paper extends results obtained for estimation of the parameters in special cases to the general p-variate case and presents the solution to the problem of what use may be made of data from incomplete multivariate samples when the interest lies in the prediction of one character from a knowledge of the rest. It is concluded that for purposes of prediction no use can be made of incomplete samples. Under certain circumstances all the observations in an incomplete sample can be used to construct improved estimators. Application of the results to multivariate normal distributions truncated on one or more characters is mentioned.