On the estimation of stochastically ordered survival functions
J. Rojo, Zheng Grace Ma · Journal of Statistical Computation and Simulation · 1996
An approach for the estimation of stochastically ordered survival functions is examined here. The one-sample problem was considered by Ma (1991),and Puri and Singh (1992). Lo (1987), treated the two-sample problem. Although some aspects of the finite sample and asymptotic distribution theory of the estimators have been presented elsewhere, no studies are available which compare the finite sample bias and mean squared error behavior of these estimators with that of their Nonparametric Maximum Likelihood (NPMLE) counterparts. Also, the case of censored data for finite sample sizes has not been considered. It is the main goal of this paper to fill these gaps. A comparison of the NPMLE estimators with those of Ma, Puri and Singh, and Lo, demonstrate that the NPMLE approach may yield, in some cases, estimators with substantial positive bias. In fact, it turns out that in the one-sample problem, the NPMLE estimator has a uniformly larger positive bias than the estimator of Ma, and Puri and Singh. Monte Carlo study results show that the estimators compare favorably with the nonparametric maximum likelihood estimators, and in some cases substantial improvements occur in terms of mean squared error and bias.