On difference of means with incomplete data

An estimate of the difference of means is obtained when sampling from a bivariate normal distribution with variances σ21 and σ22 and correlation p, where some observations on either of the variables are missing. It is shown that this estimate has desirable properties. In this paper a test of the hypothesis of the equality of means is also considered. The above estimate is adopted and three new statistics based on the difference of sample means are proposed for the test. Their empirical powers are computed for different values of p and σ21/σ22.