An unbiased estimator for the survival function of censored data

A monotonic. pointwise unbiased and uniformly consistent estimator for the survival function of failure time under the random censorship model is proposed. This estimator is closely related to the Kaplan-Meier. the Nelson-Aalen. and the reduced sample estimator. Large sample properties of the new estimator are discussed.     

NONPARAMETRIC ESTIMATORS FOR CENSORED CORRELATED DATA

ABSTRACT

In the context of failure time data, over the long run, dependent observations that might be censored are commonly encountered in practice. The main objective of this paper is to make inference about the common marginal distribution of the failure times. To this end, one nonparametric estimator, namely, the Nelson-Aalen estimator is modified to incorporate the dependence among the observations. The modified estimator is the weighted moving average (WMA) version of the existing estimator used for independent data. It has been shown that the new version is better in the sense of minimizing the one-step ahead forecast errors. Also, the new estimator can be used as a crude measure for checking independence among observations.     

A sequential scheme to estimate the optimal age replacement policy

Consider a system which is subject to failure and must be replaced when this occurs. If it costs less to replace the system in advance before failure, it may be advantageous to use an age replacement policy. However, the optimal age to replace the system is unknown if the underlying failure distribution is unknown. This paper develops a scheme to update the current estimate of the optimal age replacement policy in an on-line fashion and simultaneously controlling costs by reducing system failures.     

Generalized Supremum Tests for the Equality of Cause Specific Hazard Rates

In this paper we propose two new classes of asymptotically distribution-free Renyi-type tests for testing the equality of two risks in a competing risk model with possible censoring. This work extends the work of Aly, Kochar and McKeague [1994, Journal of American Statistical Association, 89, 994–999] and many of the existing tests for this problem belong to these newly proposed classes. The asymptotic properties of the proposed tests are investigated. Simulation studies are done to compare the performance with existing tests. A competing risks data set is analyzed to demonstrate the usefulness of the procedure.     

Improved versions of greenwood estimators under koziol-green model

ABSTRACT

It is well known that the Greenwood estimators underestimate the variances of the Nelson-Aalen estimator and the Kaplan-Meier estimator. In this article, we reveal some “improved” versions of the Greenwood estimators under the Koziol-Green model.