Inference concerning the population correlation coefficient from bivariate normal samples based on minimal observations

Summary Let (X, Y) be bivariate normally distributed with means (μ ₁,μ ₂), variances (σ ₁ ² ,σ ₂ ² ) and correlation betweenX andY equal to ρ. Let (X _i ,Y _i ) be independent observations on (X,Y) fori=1,2,...,n. Because of practical considerations onlyZ _i =min (X _i ,Y _i) is observed. In this paper, as in certain routine applications, assuming the means and the variances to be known in advance, an unbiased consistent estimator of the unknown distribution parameter ρ is proposed. A comparison between the traditional maximum likelihood estimator and the unbiased estimator is made. Finally, the problem is extended to multivariate normal populations with common mean, common variance and common non-negative correlation coefficient.