We show that the nonparametric maximum likelihood estimator (NPMLE) of a distribution function based on balanced ranked set samples is consistent, converges weakly to a Gaussian process and is asymptotically efficient. The covariance function of the limiting process is described in terms of the solution to a Fredholm integral equation of the second kind.
"Asymptotic properties of the NPMLE of a distribution function based on ranked set samples." Ann. Statist. 25 (3) 1036 - 1049, June 1997. https://doi.org/10.1214/aos/1069362737