Statistical Diagnosis of Mixture Nonlinear Location Regression Model with Skew-Normal Data

CAO Xingyun, NIE Xingfeng, WU Liucang

Acta Mathematicae Applicatae Sinica ›› 2021, Vol. 44 ›› Issue (2) : 209-225.

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Acta Mathematicae Applicatae Sinica ›› 2021, Vol. 44 ›› Issue (2) : 209-225. DOI: 10.12387/C2021016

Statistical Diagnosis of Mixture Nonlinear Location Regression Model with Skew-Normal Data

  • CAO Xingyun, NIE Xingfeng, WU Liucang
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Abstract

In the fields of economy, biomedical and environmental science, there is a kind of mixed data which is asymmetric, nonlinear and contains outliers or strong influence points. If the data is diagnosed roughly, the results may not be accurate. Therefore, the statistical diagnosis of the mixture nonlinear location regression model with the skew-normal data is studied. In this paper, by comparing the diagnosis of mixed data with the diagnosis after classification, we find that the diagnosis after classification is more accurate. Secondly, Pena distance was extended to the skew-normal nonlinear regression model, and the Likelihood distance, Cook distance and Pena distance are given to distinguish outliers or strong influence points. The results presents that Pena distance is more sensitive to outliers, and the diagnostic effect is slightly better than Likelihood distance and Cook distance. Finally, the model and method proposed in this paper are proved to be reasonable through the Monte-Carlo simulation and real data analysis.

Key words

Pena distance / mixture nonlinear location regression model / skew-normal data / statistical diagnosis

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CAO Xingyun, NIE Xingfeng, WU Liucang. Statistical Diagnosis of Mixture Nonlinear Location Regression Model with Skew-Normal Data. Acta Mathematicae Applicatae Sinica, 2021, 44(2): 209-225 https://doi.org/10.12387/C2021016

References

[1] Goldfeld S M, Quandt R E. A Markov model for switching regressions. Journal of Econometrics, 1973, 1:3-15
[2] McLachlan G, Peel D. Finite Mixture Models. New York:Wiley, 2000
[3] Yao W X, Wei Y, Yu C. Robust mixture regression models using t-distribution. Computational Statistics and Data Analysis, 2014, 71:116-127
[4] Song W X, Yao W X, Xing Y R. Robust mixture regression models fitting by laplace distribution. Computational Statistics and Data Analysis, 2014, 71:128-137
[5] Liu M, Lin T I. A skew-normal mixture regression model. Educational and Psychological Measurement, 2014, 74:139-162
[6] Pena D. A new statistic for influence in linear regression. Technometrics, 2005, 47(1):1-12
[7] 孟丽丽, 卢志义. 基于Pena距离的加权最小二乘估计的影响分析. 数理统计与管理, 2009, 28(2):252-257(M L L, L Z Y. Influence analysis of weighted least squares estimation based on Pena distance. Mathematical statistics and management, 2009, 28(2):252-257)
[8] 胡江. 基于Pena距离的非线性回归模型的影响分析. 大学数学, 2012, 28(5):80-85(H J. Influence analysis of nonlinear regression model based on Pena distance. College Mathematics, 2012, 28(5):80-85)
[9] 胡江. 基于Pena距离的几种回归模型的影响分析. 东南大学,2012(H J. Influence analysis of several regression models based on Pena distance. Southeast University, 2012)
[10] 胡江, 林金官, 赵彦勇. 基于Pena距离的广义线性回归模型的影响分析. 应用数学, 2017, 30(3):539-546(H J, L J G, Z Y Y. Influence analysis of generalized linear regression model based on Pena distance. Mathematica Applicata, 2017, 30(3):539-546)
[11] Xie F C, Wei B C, Lin J G. Homogeneity diagnostics for skew-normal nonlinear regression models. Statistics and Probability Letters, 2009, 79(6):821-827
[12] 万文, 吴刘仓, 马梦蝶. 偏正态数据下联合位置与尺度模型的统计诊断. 应用数学, 2017, 2(9):1-10(W W, W L C, M M D. Statistical diagnosis of joint position and scale model under partial normal data. Mathematica Applicata, 2017, 2(9):1-10)
[13] 李世凯, 吴刘仓, 詹金龙. 偏态数据下混合非线性回归模型的统计推断. 曲阜师范大学学报(自然科学版), 2015, 41(4):28-34(L S K, W L C, Z J L. Statistical inference of mixed nonlinear regression model with skewed data. Journal of Qufu Normal University, 2015, 41(4):28-34)
[14] Azzalini A. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 1985, 12(2):171-178
[15] Keribin C. Consistent estimate of the order of mixture models. Comptes Rendus De Lacademie Des Sciences, 1998, 62(2):49-66
[16] 王新洲. 非线性模型参数估计理论与应用. 武汉:武汉大学出版社,2002(W X Z. Theory and application of parameter estimation in nonlinear model. Wuhan:Wuhan University Press, 2002)
[17] 聂兴锋, 吴刘仓, 邢伊琦. 基于Pena距离的偏正态数据下位置回归模型的统计诊断. 应用数学, 2019, 32(2):311-318(N X F, W L C, X Y Q. Statistical diagnosis of position regression model under partial normal data based on Pena distance. Mathematica Applicata, 2019, 32(2):311-318)
[18] McLachlan G, Peel D. Finite Mixture Models. New York:John Wiley and Sons, 2000
[19] 韦博成, 林金官, 解锋昌. 统计诊断. 北京:高等教育出版社,2009(W B C, L J G, X F C. Statistical diagnosis. Beijing:Higher Education Press, 2009)
[20] Dempster A P, Laird N, Rubin D B. Maximum likelihood estimation from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, Series B, 1977, 39:1-38
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