Asymptotic properties of the NPMLE of a distribution function based on ranked set samples. (English) Zbl 0879.60037

Huang, Jian

Ann. Stat. 25, No. 3, 1036-1049 (1997).

Summary: 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.

MSC:

60G15	Gaussian processes
62G20	Asymptotic properties of nonparametric inference
60G05	Foundations of stochastic processes

Keywords:

asymptotic normality; consistency; Fredholm integral equation; nonparametric maximum likelihood estimation; ranked set sample