基于极大似然法的土壤重金属删失数据的相关性

冯旭; 孙大荃; 李仁英; 汪丽军; 黄利东

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中国环境科学 ›› 2022, Vol. 42 ›› Issue (10) : 4713-4719.

土壤污染与控制

基于极大似然法的土壤重金属删失数据的相关性

冯旭¹, 孙大荃², 李仁英¹, 汪丽军³, 黄利东¹

作者信息 +

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

Author information +

文章历史 +

摘要

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.

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.

导出引用

冯旭, 孙大荃, 李仁英, 汪丽军, 黄利东. 基于极大似然法的土壤重金属删失数据的相关性[J]. 中国环境科学. 2022, 42(10): 4713-4719

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

中图分类号： X53

参考文献

[1] Senesil G S, Baldassarre G, Senesi N, et al.Trace element inputs into soils by anthropogenic activities and implications for human health[J].Chemosphere, 1999,39(2):343-377.
[2] He Z L, Yang X E, Stoffella P J.Trace elements in agroecosystems and impacts on the environment[J].Journal of Trace Elements in Medicine and Biology, 2005,19(2):125-140.
[3] Haris M, Hamid Y, Usman M, et al.Crop-residues derived biochar:synthesis, properties, characterization and application for the removal of trace elements in soils[J].Journal of Hazardous Materials, 2021,416:126212.
[4] Suda A, Makino T.Functional effects of manganese and iron oxides on the dynamics of trace elements in soils with a special focus on arsenic and cadmium:a review[J].Geoderma, 2016,270:68-75.
[5] Laveuf C, Cornu S.A review on the potentiality of rare earth elements to trace pedogenetic processes[J].Geoderma, 2009,154(1):1-12.
[6] Ullah H, Liu G, Yousaf B, et al.A comprehensive review on environmental transformation of selenium:recent advances and research perspectives[J].Environmental Geochemistry and Health, 2019,41(2):1003-1035.
[7] Wang Z, Huang W, Pang F.Selenium in soil-plant-microbe:a review[J].Bulletin of Environmental Contamination and Toxicology, 2022, 108(2):167-181.
[8] Wendling L A, Blomberg P, Sarlin T, et al.Phosphorus sorption and recovery using mineral-based materials:sorption mechanisms and potential phytoavailability[J].Applied Geochemistry, 2013,37:157-169.
[9] 刘斌霞,王纯杰.广义指数比例风险模型下区间删失数据的贝叶斯估计[J/OL].数理统计与管理:1-9[2022-02-16].DOI:10.13860/j.cnki.sltj.20211130-025.Liu B X and Wang C J.Bayesian Estimation of Interval Censored Data with Proportional Hazards Model under Generalized Exponential Distribution[J/OL].Journal of Applied Statistics and Management:1-9[2022-02-16].DOI:10.13860/j.cnki.sltj.20211130-025.
[10] 龚鹏.地球化学矿致异常空间分析与定量评价[D].北京:中国地质大学, 2014.Gong P.Spatial analysis and quantitative evaluation of geochemical anomalies caused by ore bodies-two areas from Jiurui copper and dahutang tungsten[D].Beijing:China University of Geosciences, 2014
[11] Lyles R H, Fan D, Chuachoowong R.Correlation coefficient estimation involving a left censored laboratory assay variable[J].Statistics in Medicine, 2001,20(19):2921-2933.
[12] Kim C, Han K.Estimation of the scale parameter of the rayleigh distribution with multiply type-II censored sample[J].Journal of Statistical Computation and Simulation, 2009,79(8):965-976.
[13] Sun T, Ding Y.Copula-based semiparametric regression method for bivariate data under general interval censoring[J].Biostatistics, 2021, 22(2):315-330.
[14] Zeng D, Gao F, Lin D Y.Maximum likelihood estimation for semiparametric regression models with multivariate interval-censored data[J].Biometrika, 2017,104(3):505-525.
[15] 蔡丽馨,仲子航,杨旻,等.指定删失比例的生存数据模拟及R实现[J].中国卫生统计, 2022,39(1):143-148.Cai L X, Zhong Z H, Yang M, et al.Survival data simulation and R implementation of specified censoring ratio[J].China Health Statistics, 2022,39(1):143-148.
[16] 龙兵,张忠占.左删失恒定应力部分加速寿命试验下逆Rayleigh分布的参数估计[J].浙江大学学报(理学版), 2020,47(3):315-321.Long B, Zhang Z Z.Parameter estimation of inverse rayleigh distribution for constant-stress partially accelerated life tests with left censoring[J].Journal of Zhejiang University (Science Edition), 2020, 47(3):315-321.
[17] Fu F, Lu S, Yu Y, et al.Geostatistical analysis of heavy metals in vegetable soil from guilin city, China[J].Advanced Materials Research, 2014,1030-1032:526-531.
[18] Shao S, Hu B, Tao Y, et al.Comprehensive source identification and apportionment analysis of five heavy metals in soils in Wenzhou City, China[J].Environmental Geochemistry and Health, 2022,44(2):579-602.
[19] Yue S.The bivariate log-normal distribution for describing joint statistical properties of a multivariate storm event[J].Environmetrics, 2002,13(8):811-819.
[20] de Caritat P, Cooper M.National geochemical survey of australia:the geochemical atlas of australia:dataset[EB/OL].http://dx.doi.org/10.11636/Record.2011.020.
[21] MiaoY, Wang Y.Moderate deviation principle for maximum-likelihood estimator[J].Statistics, 2014:48.
[22] Houssineau J, Singh S S, Jasra A.Identification of multiobject dynamical systems:consistency and Fisher Information[J].SIAM Journal on Control and Optimization, 2019,57(4):2603-2627.
[23] Phadnis M A, Sharma P, Thewarapperuma N, et al.Assessing accuracy of Weibull shape parameter estimate from historical studies for subsequent sample size calculation in clinical trials with time-to-event outcome[J].Contemporary Clinical Trials Communications, 2020, 17:100548.
[24] Thomopoulos N.Statistical Distributions:Applications and parameter estimates[M].Berlin:Springer, 2017:165-166.
[25] Yan T, Leng C.A simulation study of the p1 model for directedrandom graphs[J].Statistics and Its Interface, 2015,8:255-266.
[26] Wagh Y S, Kamalja K K.Comparison of methods of estimation for parameters of generalized Poisson distribution through simulation study[J].Communications in Statistics-Simulation and Computation, 2017,46(5):4098-4112.
[27] Lima G A R.Influência de dados censurados no cálculo da concentração média das variáveis de qualidade da água DQO e fosfato[J].Engenharia Sanitaria E Ambiental, 2016,20.
[28] Newton E,Rudel R.Estimating correlation with multiply censored data arising from the adjustment of singly censored data[J].Environ Sci Technol, 2007,41(1):221-8.
[29] Chang Y-C.Efficiently implementing the maximum likelihood estimator for hurst exponent[J].Mathematical Problems in Engineering, 2014,2014:490568.
[30] Zhao Y, Frey H C.Quantification of variability and uncertainty for censored data sets and application to air toxic emission factors[J].Risk Anal., 2004,24(4):1019-1034.
[31] Ganser G H, Hewett P.An accurate substitution method for analyzing censored data[J].J.Occup.Environ.Hyg., 2010,7(4):233-244.
[32] Domthong U, Parikh C R, Kimmel P L, et al.Assessing the agreement of biomarker data in the presence of left-censoring[J].BMC Nephrology, 2014,15(1):144.
[33] Szarka A Z, Hayworth C G, Ramanarayanan T S, et al.Statistical techniques to analyze pesticide data program food residue observations[J].Journal of Agricultural and Food Chemistry, 2018, 66(27):7165-7171.
[34] Mackenzie D J, Craw D.The mercury and silver contents of gold in quartz vein deposits, Otago Schist, New Zealand[J].New Zealand Journal of Geology and Geophysics, 2005,48(2):265-278.