基于极大似然法的土壤重金属删失数据的相关性

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：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.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.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.随着删失比例的提升，MLE精确性明显优于删除法和替换法.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.

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

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.