On Estimators Obtained From a Sample Augmented by Multiple Regression

A sample of N observations is taken from a p + 1 variate normal distribution. The first N observations include values on all p + 1 variates, whereas the remaining N‐n observations include values for p of the variates only. This paper reviews the properties of the estimators that use the N complete observations on the p variates to improve estimation of the mean and variance of the variate with only n observations. In particular, the relationship of suggested estimators to maximum likelihood estimators, corrected for bias, is given. The general advantages and limitations of such estimators are discussed.