Distribution of the \(ML\) estimate of the correlation coefficient of two- dimensional normal data with missing values in one variable (Q1897870)

There has been considerable recent interest in the whole range of unsolved problems concerning the analysis of data with missing values. As one of the problems, we specifically mention evaluation of the distributions of statistical parameters which are required when testing significance and constructing confidence limits. In this work a two- dimensional random sample from a normal population with missing values in one variable is considered and the distribution of the maximum likelihood (ML) estimate of the correlation coefficient is calculated. In the case of uncorrelated data the density function of this distribution (expressed in terms of the hypergeometric function) is found. Questions dealing with testing the significance of the correlation coefficient are discussed as well.