A Correlation Model Useful in the Study of Twins

Abstract Let (X, Y) be bivariate normally distributed with mean (μ, v), var(X) = var(Y) = σ2, and correlation between X and Y equal to ρ. Let (X i , Y i ) be independent observations on (X, Y) for i = 1, 2, · · ·, n. Because of practical considerations we observe only Z i = min(X i , Y i ), i = 1, 2, · · ·, n. We are concerned with estimation and testing procedures when the parameter ρ is unknown. This model will be useful in certain studies of twins.