Estimators of the correlation coefficient in the bivariate exponential distribution

A finite-support constraint on the parameter space is used to derive a lower bound on the error of an estimator of the correlation coefficient in the bivariate exponential distribution. The bound is then exploited to examine optimality of three estimators, each being a nonlinear function of moments of exponential or Rayleigh observables. The estimator based on a measure of cosine similarity is shown to be highly efficient for values of the correlation coefficient greater than 0.35; for smaller values, however, it is the transformed Pearson correlation coefficient that exhibits errors closer to the derived bound.