Large Sample Properties of MLE of the Distribution Function with Incomplete Data
Liping Liu · Acta Scicentiarum Naturalum Universitis Pekinesis · 1996
In 1974 Turnbull proposed the nonparametric MLE of the distributionfunction with incomplete data which may be censored either from above or below.This estimator is also self-consistent.When the data are grouped,we showed thatthe distribution function of interest and the distribution functions of the two censor-ing variables satisfy an equation system.By studying the uniqueness of the solutionof this equation system,we proved the strong consistency of the Turnbull estima-tor.We also proved the asymptotic normality and the law of the iterated logarithm,and have given the matrix representation of the asymptotic covariance matrix andthe accurate upper bounds of the convergence rate in the law of the iterated loga-rithm.