A nonparametric Bayes estimator of the survival function is derived for right censored data where additional observations from the residual distribution are available. The estimation is motivated by data on contamination concentrations for chromium from one of the EPA's toxic waste sites. The residual sample can be produced by hot spot sampling, where only samples above a given threshold value are collected. The Dirichlet process is used to formulate prior information about the chromium contamination, and we compare the Bayes estimator of the mean concentration level to other estimators currently considered by the EPA and other sources. The Bayes estimator generally out- performs the other estimators under various cost functions. The limiting distribution is the nonparametric maximum likelihood estimator, which is identical to the Kaplan-Meier estimator for concentration values observed below the residual sample threshold. Robustness of the Bayes estimate is examined with respect to misspecification of the prior and its sensitivity to the censoring distribution.
Copyright © 2000 Taylor & Francis.
The definitive version is available at: https://www.tandfonline.com/doi/abs/10.1080/01621459.2000.10474308
Kvam, Paul H., Ram C. Tiwari, and Jyoti N. Zalkikar. "Nonparametric Bayes Estimation of Contamination Levels Using Observations from the Residual Distribution." Journal of the American Statistical Association 95, no. 452 (2000): 1119-1126. doi:10.1080/01621459.2000.10474308.
Kvam, Paul H.; Tiwari, Ram C.; and Zalkikar, Jyoti N., "Nonparametric Bayes Estimation of Contamination Levels using Observations from the Residual Distribution" (2000). Math and Computer Science Faculty Publications. 198.