Estimating the mean and standard deviation of environmental data with below detection limit observations: Considering highly skewed data and model misspecification

Shoari, Niloofar; Dubé, Jean-Sébastien; Chenouri, Shojaeddin

doi:10.1016/j.chemosphere.2015.07.009

Cited by 27 publications

(39 citation statements)

References 22 publications

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“…In the present study, the statistic of interest is the mean,

{true \bar{x}}^{*}

, and standard deviation,

s^{*}

, of the bootstrap sample. Details regarding the computation of the aforementioned estimators can be found in Hewett and Ganser , Shoari et al and Helsel .…”

Section: Methodsmentioning

confidence: 99%

“…In studies based on Monte Carlo simulations, the bias and uncertainty are quantifiable because the true values of parameters are known. Some examples of Monte Carlo simulation studies based on left‐censored data can be found in Hewett and Ganser , Kroll and Stedinger , Sinha et al , European Food and Safety Authority , and Shoari et al , among others. Typically, the mean square error (MSE) is used as a criterion to reflect both bias and uncertainty of the estimates in each simulation scenario.…”

Section: Introductionmentioning

confidence: 99%

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An investigation of the impact of left‐censored soil contamination data on the uncertainty of descriptive statistical parameters

Shoari¹,

Dubé²

2016

Enviro Toxic and Chemistry

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Left-censored concentration data are frequently encountered because measuring instruments cannot detect concentrations below the instrument detection limit. For statistical analysis of left-censored data, the environmental literature mainly refers to the following methods: maximum likelihood estimator, regression on order statistics using log-normal and gamma assumption (rROS and GROS, respectively), and Kaplan-Meier. A number of simulation experiments examined the performance of these methods in terms of bias and/or mean square error. However, no matter which method is adopted, some uncertainty is introduced into outcomes because all that is known about a left-censored observation is that the concentration falls between 0 and the detection limit. The data used in the present study come from analysis of soil samples collected for a site characterization in Montreal, Canada. Employing nonparametric bootstrap, the authors quantify the uncertainty and bias in the mean and standard deviation estimates obtained by the maximum likelihood estimation (under log-normal, Weibull, and gamma distributions), rROS, GROS, and Kaplan-Meier methods. First, the authors demonstrate that the highest uncertainty is associated with the maximum likelihood estimator under log-normality and Weibull assumptions, whereas a gamma assumption leads to estimates with less uncertainty. Second, the authors show that although an increase in sample size improves the uncertainty, it reduces the bias only in the rROS, GROS, and Kaplan-Meier methods. Finally, comparing percentage uncertainty in the mean of contaminant data, the authors illustrate that adopting an inappropriate estimator results in large uncertainties. Environ Toxicol Chem 2016;35:2623-2631. © 2016 SETAC.

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“…In the present study, the statistic of interest is the mean,

{true \bar{x}}^{*}

, and standard deviation,

s^{*}

, of the bootstrap sample. Details regarding the computation of the aforementioned estimators can be found in Hewett and Ganser , Shoari et al and Helsel .…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An investigation of the impact of left‐censored soil contamination data on the uncertainty of descriptive statistical parameters

Shoari¹,

Dubé²

2016

Enviro Toxic and Chemistry

Self Cite

View full text Add to dashboard Cite

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“…This topic is only partially accounted for in literature (e.g., Mitra and Kundu, 2008;Shoari et al, 2015). On one hand, the ML approach can certainly be used when data are not normally distributed, and the sample size is large enough.…”

Section: Introductionmentioning

confidence: 99%

“…Authors prefer the Weibull distribution because of its flexibility and ability to adapt to real data. In Shoari et al (2015), there are critical comments about low robustness of the Weibull distribution considering a misspecification of the model distribution, especially for high values of skewness γ. However, simulation results showed that when the sample size is small, and skewness of the distribution is high (γ > 2), there can be numerical difficulties with parameters estimates, which can give an impression of low robustness of the Weibull distribution to the model misspecification.…”

Section: Introductionmentioning

confidence: 99%

“…It is based on the assumption that the censored sample has a known distribution. In order to estimate unknown parameters of the distribution, the maximum likelihood (ML) method (Barndorff-Nielsen and Cox, 1994;Lehmann and Casella, 1998;Lehmann and Romano, 2005), and the approach based on the regression on order statistics (Helsel, 2012;Shoari et al, 2015) are often used. When analyzing skewed left-censored samples, the log-normal, the Weibull, the exponential, the generalized exponential, and the gamma distributions are usually used as model distributions (Fusek andMichálek, 2012b, 2015b;Gupta and Kundu, 1999;Helsel, 2012;Hogg et al, 2005;Mitra and Kundu, 2008;Schmoyeri et al, 1996).…”

Section: Introductionmentioning

confidence: 99%

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Left-Censored Samples from Skewed Distributions: Statistical Inference and Applications

Fusek

Michálek

2018

Acta Univ. Agric. Silvic. Mendelianae Brun.

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Left-censored data occur frequently in many areas. At present, researchers pay attention to skewed censored distributions more frequently. This paper deals with statistical inference of type I multiply left-censored Weibull and exponential distributions. It suggests a computational procedure for calculation of maximum likelihood estimates of the parameters. The expected Fisher information matrix for estimation of variances of estimated parameters is introduced. The estimates are then used for construction of confidence intervals for the expectation using the maximum likelihood method. Asymptotic tests for comparison of distributions (expectations respectively) of two independent left-censored Weibull samples are proposed. Furthermore, asymptotic tests for assessing suitability of reduction of the Weibull distribution to the exponential distribution are introduced. Finally, the left-censored exponential distribution is briefly described. Methods derived in this paper are illustrated on elemental carbon measurements, and can be applied in analysis of real environmental and/or chemical data.

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Toward improved analysis of concentration data: Embracing nondetects

Shoari

Dubé

2018

Enviro Toxic and Chemistry

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Various statistical tests on concentration data serve to support decision-making regarding characterization and monitoring of contaminated media, assessing exposure to a chemical, and quantifying the associated risks. However, the routine statistical protocols cannot be directly applied because of challenges arising from nondetects or left-censored observations, which are concentration measurements below the detection limit of measuring instruments. Despite the existence of techniques based on survival analysis that can adjust for nondetects, these are seldom taken into account properly. A comprehensive review of the literature showed that managing policies regarding analysis of censored data do not always agree and that guidance from regulatory agencies may be outdated. Therefore, researchers and practitioners commonly resort to the most convenient way of tackling the censored data problem by substituting nondetects with arbitrary constants prior to data analysis, although this is generally regarded as a bias-prone approach. Hoping to improve the interpretation of concentration data, the present article aims to familiarize researchers in different disciplines with the significance of left-censored observations and provides theoretical and computational recommendations (under both frequentist and Bayesian frameworks) for adequate analysis of censored data. In particular, the present article synthesizes key findings from previous research with respect to 3 noteworthy aspects of inferential statistics: estimation of descriptive statistics, hypothesis testing, and regression analysis.

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Estimating the mean and standard deviation of environmental data with below detection limit observations: Considering highly skewed data and model misspecification

Cited by 27 publications

References 22 publications

An investigation of the impact of left‐censored soil contamination data on the uncertainty of descriptive statistical parameters

An investigation of the impact of left‐censored soil contamination data on the uncertainty of descriptive statistical parameters

Left-Censored Samples from Skewed Distributions: Statistical Inference and Applications

Toward improved analysis of concentration data: Embracing nondetects

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