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应用数学学报  2012, Vol. Issue (4): 677-692    DOI:
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纵向数据半参数Beta回归模型的影响分析
赵为华1,2, 李泽安3, 徐相建2
1. 华东师范大学金融与统计学院, 上海 200241;
2. 南通大学理学院, 南通 226007;
3. 南通大学计算机学院, 南通 226007
Influence Analysis for Semi-parametric Beta Regression Model with Longitudinal Data
ZHAO Weihua1,2, LI Zean3, XU Xiangjian2
1. School of Finance and Statistics, East China Normal University, Shanghai 200241;
2. School of Science, NanTong University, JiangSu NanTong 226007;
3. School of Computer, NanTong University, JiangSu NanTong 226007
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摘要 本将随机效应当作是缺失数据, 基于Q函数和EM算法并利用P-样条拟合非参数部分, 得到了纵向数据半参数Beta回归模型估计方法.基于数据删除模型, 我们得到了模型参数部分的广义Cook距离以及非参数部分的广义DFIT. 此外, 本文还研究了 在四种不同扰动情形下模型的局部影响分析, 得到了相应的影响矩阵. 最后, 我们通过两个数值实例验证了所得诊断统计量的有效性.
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赵为华
李泽安
徐相建
关键词Beta 回归   纵向数据   半参数   影响分析   P-样条   EM 算法     
Abstract: This paper present several case-deletion as well as local influence measures for assessing the influence of an observation for Semi-parametric Beta Regression Model with Longitudinal Data. The essential idea is to treat the latent random effects in the model as missing data and get the estimate algorithm by adding penalized spline to estimate the non-parameters. We generate generalized Cook distance and generalized DFIT for the parametric and nonparametric part respectively based case-deletion model by Q-function. Four different perturbation schemes are discussed. Two numeric examples are presented to illustrate the results.
Key wordsBeta regression   longitudinal data   semi-parametric   influence analysis   P-spline   EM algorithm   
收稿日期: 2009-01-04;
基金资助:国家自然科学基金(11171112)和南通大学自然科学基金(10Z008)资助项目.
引用本文:   
赵为华,李泽安,徐相建. 纵向数据半参数Beta回归模型的影响分析[J]. 应用数学学报, 2012, (4): 677-692.
ZHAO Weihua,LI Zean,XU Xiangjian. Influence Analysis for Semi-parametric Beta Regression Model with Longitudinal Data[J]. Acta Mathematicae Applicatae Sinica, 2012, (4): 677-692.
 
[1] Zhu H, Lee S. Local Influence for Incomplete-data Models. J. Journal of the Royal Statistical Society, Series B, 2001, 63: 111-126
[2] Cook R. Detection of Influential Observation in Linear Regression. J. Technometrics, 1977, 19: 15-18
[3] Cook R. Assessment of Local Influence. J. Journal of the Royal Statistical Society (Series B), 1986, 48: 133-169
[4] Wing F, Zhu Z, Wei B, He X. Influence Diagnostics and Outlier Tests for Semi-parametric Mixed Models. J. Journal of the Royal Statistical Society (Series B), 2002, 64: 565-579
[5] Zhu H, Lee S. Local Influence for Generalized Linear Mixed Models. J. the Canadian Journal of Statistics, 2003, 31: 1-17
[6] 张浩, 朱仲义. 半参数广义线性混合效应模型的影响分析. kaishu 应用数学学报, 2007, 30: 743-759 REF (Zhang H, Zhu Z. Influence Analysis of Generalized Partially Linear Mixed Models. Acta Mathematicae Applicatae Sinica, 2007, 30: 743-759)
[7] Ferrari S, Cribari-Neto F. Beta Regression for Modeling Rates and Proportions. J. Journal of Applied Statistics, 2004, 31: 799-815
[8] Espinheira P, Ferrari S, Cribari-Neto F. Influence Diagnostics in Beta Regression. J. Computational Statistics and Data Analysis, 2008, 52: 4417-4431
[9] 李爱萍, 解锋昌, 刘应安. Beta回归模型的影响诊断. kaishu 高校应用数学学报, 2007, 22: 293-300 REF (Li A, Xie F, Liu Y. Influence Diagnostics in Beta Regression Model. J. Applied Mathematics a Journal of Chinese Universities, 2007, 22: 293-300
[10] Yu Y, Ruppert D. Penalized Spline Estimation for Partially Linear Single-index Models. J. Journal of the American Statistical Association, 2002, 97: 1042-1054
[11] McGilchrist C. Estimation in Generalized Mixed Models. J. Journal of the Royal Statistical Society (Series B), 1994, 56: 61-69
[12] Dempster A, Laird N, Rubin D. Maximum Likelihood from Incomplete Data via the EM Algorithm (with discussion). J. Journal of the Royal Statistical Society (Series B), 1977, 39: 1-38
[13] Wu, C. On the Convergence Properties of the EM Algorithm. J. Annal of Statistics, 1983, 11: 95-103
[14] Tanner M. Tools for Statistical Inference: Observed Data and Data Augmentation. Berlin: Springer-Verlag, 1993
[15] Banerjee M, Frees E. Influence Diagnostics for Linear Longitudinal Models. J. Journal of the American Statistical Association, 1997, 92: 999-1005
[16] Griffiths W, Hill R. Judge G. Learning and Practicing Econometrics. New York: Wiley, 1993
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