半变系数再生散度混合效应模型的影响分析
Influence Analysis of Semivarying Coefficient Reproductive Dispersion Mixed Models
摘要:

本文把随机效应看作缺失数据并利用P-样条拟合非参数部分，应用Monte Carlo EM 加速算法得到半变系数再生散度混合效应模型的未知参数的估计，同时利用Q函数，得到了模型的广义Cook距离。此外，本文还研究了三种不同扰动情形的局部影响分析，得到了相应的影响矩阵。最后，通过一个实际例子验证了所提出的诊断统计量的有效性。

Abstract: This paper proposes several case-deletion as well as local influence measures for assessing the influence of an observation for semivarying coefficient reproductive dispersion mixed models. The essential idea is to treat the latent random effects in the model as missing data and estimate unknown parameters by acceleration of Monte Carlo EM algorithm. Onthe basis of the Q-function which is associated with the conditional expectation of the complete-data log-likelihood, we generate generalized Cook Distance. Moreover, three different perturbation schemes are discussed. Finally，one real illustrative example is presented to prove the methodology.

 

文章引用：姜荣, 杨筱菡, 钱伟民. 半变系数再生散度混合效应模型的影响分析[J]. 统计学与应用, 2012, 1(2): 37-43. http://dx.doi.org/10.12677/SA.2012.12008

参考文献

[1] R. D. Cook, S. Weisberg. Residual and influence in regression. New York: Chapman and Hall, 1982.
[2] G. Seber, C. J. Wild. Nonlinear Regression. New York: Wiley, 1989.
[3] 姜荣, 邵明江, 钱伟民. 半参数非线性模型中的t-型估计和影响分析[J]. 华东师范大学学报(自然科学版), 2011, 3: 1-11.
[4] R. J. Beckman, C. J. Nachtsheim and R. D. Cook. Diagnostics for mixed-model analysis of variance. Technometrics, 1987, 29(4): 413-426.
[5] 张浩, 朱仲义. 半参数广义线性混合效应模型的影响分析[J]. 应用数学学报, 2007, 30(4): 773-756.
[6] B. Jorgensen. The theory of dispersion models. London: Chap- man and Hall, 1997
[7] 唐年胜,韦博成. 非线性再生散度模型[M]. 北京: 科学出版社, 2007.
[8] X. H. Lin, D. W. Zhang. Inference in generalized addi-tive mixed models by using smoothing splines. Journal of the Royal Statis- tical Society, Series B, 1999, 61(2): 381-400.
[9] C. E. McCulloch. Maximum likelihood algorithm for general- ized linear mixed models. Journal of the American Statistical Association, 1997, 92(437): 162-170.
[10] 罗季. Monte Carlo EM 加速算法[J]. 应用概率统计, 2008, 24(3): 311-318.
[11] Y. Yu, D. Ruppert. Penalized spline estimation for partially linear single-index models. Journal of the American Statistical Association, 2002, 97(460): 1042-1054.
[12] H. T. Zhu, S. Y. Lee, B. C. Wei and J. Zhu. Case-deletion meas- ures for models with incomplete data. Biometrika, 2001, 88(3): 727-737.
[13] A. Gelman, G. O. Roberts and W. R. Gilks. Efficient metropolis jumping rules. Bayesian statistics 5, Oxford: Oxford University Press, 1995.
[14] M. Davison, D. M. Giltinan. Nonlinear models for repeated meas- urement data. London: Chapman and Hall, 1995.
[15] 韦博成, 林金官, 解锋昌. 统计诊断[M]. 北京: 高等教育出版社, 2009.

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