Order-Restricted Estimation of the New Better Than Used in Expectation and Decreasing Mean Residual Life Functions Under Censoring

• Activity Number: 188
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ganesh Bahadur Malla*+ and Hari Mukerjee
• Companies: Xavier University and Wichita State University
• Keywords: Order restricted estimator ; Kaplan-Meier estimator ; Uniformly strongly consistent ; Mean residual life function ; Weak convergence ; Censoring

Abstract

In survival analysis and in the analysis of the life tables an important biometric function of interest is the mean residual life function (MRLF) whose value at age t is the average future life time given that a subject has survived till time t. Two important classes of the MRLFs are the 'New Better than Used in Expectation (NBUE) class' and 'Decreasing Mean Residual Life (DMRL) class'. In this paper we consider the problem of estimation the MRLFs in the NBUE and DMRL classes under random censoring. We have proven that our "order restricted estimators", one for each class, are uniformly strongly consistent, and converge weakly to a Gaussian process. By simulation, we have also shown that our estimators are better than the Kaplan-Meier estimator in terms of asymptotic mean sums of squares. Several applications of our estimators have been provided.