基于极大似然法的土壤重金属删失数据的相关性

0567928 - BC 2023 RIV CN chi J - Journal Article
Feng, X. - Sun, Daquan - Li, R.-Y. - Wang, L.-J. - Huang, L.-D.
基于极大似然法的土壤重金属删失数据的相关性.
[Correlation of soil heavy metal censored data based on maximum likelihood method.]
Zhongguo Huanjing Kexue/China Environmental Science. Roč. 42, č. 10 (2022), s. 4713-4719. ISSN 1000-6923
Institutional support: RVO:60077344
Keywords : bivariate log-normal distribution * censored data * correlation coefficient * heavy metal * maximum likelihood estimation * soil
OECD category: Agriculture
Method of publishing: Limited access
https://kns.cnki.net/kcms/detail/detail.aspx?doi=10.19674/j.cnki.issn1000-6923.20220616.001

土壤环境中部分样本重金属的浓度常处于痕量级别而低于检测方法的检测限（limit of detection/LOD），因此难以定量
其浓度，此类含有低于检测限信息的土壤样本数据属于左删失数据，且该类数据常符合对数正态分布，目前为止对单指标删
失数据的参数估计较为常见，但鲜有对二维删失数据相关性估计的报道，本文基于极大似然法（MLE），通过构建不同情形
下的似然函数，提出了删失数据相关性估计的方法｡分别研究了样本容量､删失比例､总体相关系数与干扰项等因素对估计值准
确性的影响｡同时，将 MLE 与替换法（通常将删失部分替换为 LOD 或 LOD/2）和删除法（直接将删失部分删除）做对比，
检测了 MLE 的精准度｡以澳大利亚土壤普查数据作为实例对方法进行了实例应用｡结果表明:（1）样本容量越大，研究中的
MLE 的结果越准确，当样本容量达到 2000 时，估计值具有较好的稳定性，且受删失比例影响较小｡（2）MLE 的相关系数估
计值随删失比例（0%~90%）与总体相关系数变化程度较小，具有渐进无偏性和一致性｡（3）添加干扰项对 MLE 的准确性影
响较小，表明其具有较强的鲁棒性｡（4）随着删失比例的提升，MLE 精确性明显优于删除法和替换法｡（5）实际数据的应用
结果表明澳大利亚土壤普查数据中，Ag 与 Hg 有着较高的相关性，Hg 与 Hf 之间相关系数几乎为 0。本研究方法有较好的估
计性能，实现了土壤环境痕量物质信息的合理利用，为该领域删失数据的相关系数估计工作提供了可行的方法。

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.
Permanent Link: https://hdl.handle.net/11104/0339285