非线性联合均值方差模型的统计分析
Statistical Analysis for Nonlinear Joint Mean and Variance Models
DOI: 10.12677/SA.2014.32010, PDF, HTML, 下载: 2,847  浏览: 7,732  国家自然科学基金支持
作者: 周梦齐, 徐登可, 杨佳红, 王梦滢：浙江农林大学统计系，杭州
关键词: 非线性联合均值方差模型；异方差；Gauss-Newton；极大似然估计；Nonlinear Joint Mean and Variance Models； Heteroscedasticity； Gauss-Newton； Maximum Likelihood Estimate
摘要: 在提出非线性均值方差模型的基础上，研究了该模型中未知参数的估计问题。主要是基于Gauss-Newton迭代算法给出该模型中未知参数的极大似然估计。通过大量随机模拟实验验证了所提出方法的有效性。最后，结合实际问题数据验证了该模型与方法具有实用性和可行性。
Abstract: We propose nonlinear joint mean and variance models in this paper and investigate the estimate for unknown parameters in the model based on Gauss-Newton iterative algorithm. Furthermore, we make some simulations to show that the proposed procedure works satisfactorily. Lastly, two real examples are presented to illustrate the proposed methodology.
文章引用：周梦齐, 徐登可, 杨佳红, 王梦滢. 非线性联合均值方差模型的统计分析[J]. 统计学与应用, 2014, 3(2): 68-75. http://dx.doi.org/10.12677/SA.2014.32010

参考文献

[1] White, H. (1980) A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Journal of the Econometric Society, 48, 817-838.
[2] Andrews Donald, W.K. (1991) Heteroscedasticity and autocorrelation consistent covariance matrix estimation. Journal of the Econometric Society, 59, 817-858.
[3] Smyth, G.K. (2002) An efficient algorithm for REML in heteroscedastic Regression. Journal of Graphical Statistics, 11, 836-847.
[4] Park, R.E. (1966) Estimation with heteroscedastic error terms. Econometrica, 34, 888.
[5] Harvey, A.C. (1976) Estimating regression models with multiplicative heteroscedasticity. Econometrica, 44, 460-465.
[6] Aitkin, M. (1987) Modelling variance heterogeneity in normal regression using GLIM. Applied Statistics, 36, 332-339.
[7] Verbyla, A.P. (1993) Modelling variance heterogeneity: Residual maximum likelihood and diagnostics. Journal of the Royal Statistical Society: Series B, 52, 493-508.
[8] Wu, L.C. and Li, H.Q. (2012) Variable selection for joint mean and dispersion models of the inverse gaussian distribution. Metrika, 75, 795-808.
[9] Xu, D.K., Zhang, Z.Z. and Wu, L.C. (2014) Variable selection in high-dimensional double generalized linear models. Statistical Papers, 55, 327-347.
[10] 吴刘仓, 黄丽, 戴琳(2012) Box-Cox 变换下联合均值与方差模型的极大似然估计. 统计与信息论坛, 5, 3-8.
[11] 马婷, 吴刘仓, 黄丽(2013) 基于偏正态分布联合位置, 尺度与偏度模型的极大似然估计. 数理统计与管理, 3, 433-439.
[12] 徐登可, 张忠占, 张松, 张蕾 (2012) 妊娠期高血压疾病危险因素的统计分析. 应用概率统计, 2, 134-142.
[13] 贝茨, 沃茨, 著, 韦博成, 等, 译 (1997) 非线性回归分析及其应用. 中国统计出版社, 北京.

为你推荐