Correlation of soil heavy metal censored data based on maximum likelihood method

FENG Xu; SUN Da-quan; LI Ren-ying; WANG Li-jun; HUANG Li-dong

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China Environmental Science ›› 2022, Vol. 42 ›› Issue (10) : 4713-4719.

Soil Pollution Control

Correlation of soil heavy metal censored data based on maximum likelihood method

FENG Xu¹, SUN Da-quan², LI Ren-ying¹, WANG Li-jun³, HUANG Li-dong¹

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Abstract

Based on the maximum likelihood method (MLE), the current work proposed a new method for estimating the correlation of censored data thorough constructing the likelihood function under different scenarios. The effects of sample size, censorship ratio, population correlation coefficient and disturbance term on the accuracy of the estimated values were studied. At the same time, the accuracy of MLE was tested by comparing MLE with substitution method (usually replacing the censored part with LOD or LOD/2) and deletion method (directly delete the censored part). The methodology was tested using the Australian census soil data. The results showed that the larger the sample size, the more accurate the MLE results would be. When the sample size reaches 2000, the estimated value has a better stability and is less affected by the censorship ratio. The estimated correlation coefficient of MLE varies less with the censorship ratio (0%~90%) or the population correlation coefficient, demonstrating gradual unbiasedness and consistency. The addition of disturbance terms has less impact on the accuracy of MLE, indicating its strong robustness. The MLE is significantly accurate than that of the deletion and substitution methods. The application of the experimental data showed that in the Australian survey data, Ag and Hg have a high correlation, and the correlation coefficient between Hg and Hf is almost 0.

Key words

bivariate log-normal distribution / censored data / correlation coefficient / heavy metal / maximum likelihood estimation / soil

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FENG Xu, SUN Da-quan, LI Ren-ying, WANG Li-jun, HUANG Li-dong. Correlation of soil heavy metal censored data based on maximum likelihood method[J]. China Environmental Science. 2022, 42(10): 4713-4719

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