Estimating Mean Concentration Under Transformation for Environment Data With Detection Limits


Shumway, R.H.; Azari, A.S.; Johnson, P.   (1989, ASQC and the American Statistical Association)   University of California, Davis, CA

Technometrics    Vol. 31    No. 3
QICID: 9408    August 1989    pp. 347-356
List $10.00
Member $5.00

This article is not available online. Contact us to receive a scan of the archive, in PDF format.

Article Abstract

The reporting procedures for potentially toxic pollutants are complicated by the fact that concentrations are measured using small samples that include a number of observations lying below some detection limit. Furthermore, there is often a small number of high concentrations observed in combination with a substantial number of low concentrations. This results in small, nonnormally distributed censored samples. This article presents maximum likelihood estimators for the mean of a population, based on censored samples that can be transformed to normality. The method estimates the optimal power transformation in the Box-Cox family by searching the censored-data likelihood. Maximum likelihood estimators for the mean in the transformed scale are calculated via the expectation-maximization algorithm. Estimates for the mean in the original scale are functions of the estimated mean and variance in the transformed population. Confidence intervals are computed using the delta method and the nonparametric percentile and bias-corrected percentile versions of Efron's bootstrap. A simulation study over sampling configurations expected with environmental data indicates that the delta method, combined with a reliable value for the power transformation, produces intervals with better coverage properties than the bootstrap intervals.


Bootstrap methods,Box-Cox model,Censored data,Statistical methods,Algorithm,Maximum likelihood estimate (MLE)

Browse QIC Articles Chronologically:     Previous Article     Next Article

New Search

Featured advertisers

ASQ is a global community of people passionate about quality, who use the tools, their ideas and expertise to make our world work better. ASQ: The Global Voice of Quality.