Geostatistical estimation and prediction for censored responses

José A. Ordoñez, Dipankar Bandyopadhyay, Victor H. Lachos, Celso R.B. Cabral

Research output: Contribution to journalReview articlepeer-review

3 Scopus citations

Abstract

Spatially-referenced geostatistical responses that are collected in environmental sciences research are often subject to detection limits, where the measures are not fully quantifiable. This leads to censoring (left, right, interval, etc.), and various ad hoc statistical methods (such as choosing arbitrary detection limits, or data augmentation) are routinely employed during subsequent statistical analysis for inference and prediction. However, inference may be imprecise and sensitive to the assumptions and approximations involved in those arbitrary choices. To circumvent this, we propose an exact maximum likelihood estimation framework of the fixed effects and variance components and related prediction via a novel application of the Stochastic Approximation of the Expectation Maximization (SAEM) algorithm, allowing for easy and elegant estimation of model parameters under censoring. Both simulation studies and application to a real dataset on arsenic concentration collected by the Michigan Department of Environmental Quality demonstrate the advantages of our method over the available naïve techniques in terms of finite sample properties of the estimates, prediction, and robustness. The proposed methods can be implemented using the R package CensSpatial.

Original languageEnglish (US)
Pages (from-to)109-123
Number of pages15
JournalSpatial Statistics
Volume23
DOIs
StatePublished - Mar 2018

Bibliographical note

Funding Information:
We would like to thank the Editor, Associate Editor and two referees for their constructive comments, which led to a significantly improved version of this manuscript. This paper was written while Celso R.B. Cabral was a visiting professor in the Department of Statistics at the University of Campinas, Brazil. The research of Jose A. Ordoñez was supported by CAPES . Bandyopadhyay acknowledges partial support from grants R03DE023372 , R01DE024984 and P30CA016059 (VCU Massey Cancer Center Support Grant) from the US National Institutes of Health. Celso R.B. Cabral acknowledges the support from FAPESP (Grant 2015/20922-5 ) and CNPq-Brazil (Grants 167731/2013-0 and 447964/2014-3 ). We also thank Jaymie Meliker for providing access to the arsenic contamination dataset.

Funding Information:
We would like to thank the Editor, Associate Editor and two referees for their constructive comments, which led to a significantly improved version of this manuscript. This paper was written while Celso R.B. Cabral was a visiting professor in the Department of Statistics at the University of Campinas, Brazil. The research of Jose A. Ordoñez was supported by CAPES. Bandyopadhyay acknowledges partial support from grants R03DE023372, R01DE024984 and P30CA016059 (VCU Massey Cancer Center Support Grant) from the US National Institutes of Health. Celso R.B. Cabral acknowledges the support from FAPESP (Grant 2015/20922-5) and CNPq-Brazil (Grants 167731/2013-0 and 447964/2014-3). We also thank Jaymie Meliker for providing access to the arsenic contamination dataset.

Keywords

  • Censored geostatistical data
  • Kriging
  • Limit of detection (LOD)
  • SAEM algorithm

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