基于一类重尾分布的函数型线性回归模型的稳健性估计
|
摘要
假定随机误差分布来自具有重尾特征的scale mixtures of normal分布族,运用贝叶斯方法研究了函数型线性回归模型的稳健性估计,其中模型的响应变量为标量,解释变量为函数型变量.数值模拟结果表明:当响应变量的观测数据存在离群值时,建立的方法得到的模型参数的估计,要优于正态分布假定下的模型参数的估计.
It gives Bayesian robust estimations of functional linear regression models, where the response is a scalar and the predictor is functional, by applying a class of heavy-tailed scale mixtures of normal distributions for random measurement errors. The numerical results showed that: the estimations of the model parameters using scale mixtures of normal distributions outperform the estimations using normal distributions.
It gives Bayesian robust estimations of functional linear regression models, where the response is a scalar and the predictor is functional, by applying a class of heavy-tailed scale mixtures of normal distributions for random measurement errors. The numerical results showed that: the estimations of the model parameters using scale mixtures of normal distributions outperform the estimations using normal distributions.
引文
[1] Ramsay J O, and Silverman B W. Functional Data Analysis[M](2nd ed.). Springer, New York,USA, 2005.
[2] Ramsay J O, and Silverman B W.函数型数据分析[M](第二版影印版).科学出版社,北京,2006.
[3] Ferraty F, and Vieu P. Nonparametric Functional Data Analysis:Theory and Practice[M].Springer New York USA, 2006.
[4] Koenker R, and Bassett G. JR. Regression quantiles[J]. Econometrica, 1978, 46:33-50.
[5] Cardot H, Crambes C, and Sarda P. Quantile regression when the covariates are functions[J].Journal of Nonparametric Statistics, 2005, 17:841-856.
[6] Ferraty F, Rabhi A, and Vieu P. Conditional quantiles for dependent functional data with application to the climatic El Nino phenomenon[J]. Sankhya, 2005, 67:378-398.
[7] Kato K. Estimation in functional linear quantile regression[J]. The Annals of Statistics, 2012,40(6):3108-3136.
[8] Lu Y, Du J, and Sun Z. Functional partially linear quantile regression model[J]. Metrika, 2014,77:317-332.
[9] Tang Q, and Kong L. Quantile regression in functional linear semiparametric model[J]. Statistics,2017, 51(6):1342-1358.
[10] Zhou J, Du J, and Sun Z. M-estimation for partially functional linear regression model based on splines[J]. Communications in Statistics, 2015, 45(21):6436-6446.
[11] Boente G, and Vahnovan A. Robust estimators in semi-functional partial linear regression models[J]. Journal of Multivariate Analysis, 2017, 154:59-84.
[12] Andrews D F, and Mallows C L. Scale mixtures of normal distributions[J]. Journal of the Royal Statistical Society, Series B, 1974, 36:99-102.
[13] Liu C. Bayesian robust multivariate linear regression with incomplete data[J]. Journal of the American Statistical Association, 1996, 91:1219-1227.
[14] Lange K, and Sinsheimer J. Normal/independent distributions and their applications in robust regression[J]. Journal of Computational and Graphical Statistics, 1993, 2:175-198.
[15] Choy S T B, and Smith A F M. Hierarchical models with scale mixtures of normal distributions[J]. Test, 1997, 6:205-221.
[16] Rosa G J M, Gianola D, and Padovani C R. Bayesian longitudinal data analysis with mixed models and thick-tailed distributions using MCMC[J]. Journal of Applied Statistics 2004, 31:855-873.
[17] Meza C, Osorio F, and la Cruz R D. Estimation in nonlinear mixed-effects models using heavytailed distributions[J]. Statistics and Computing 2012, 22:121-139.
[18] De la Cruza R. Bayesian analysis for nonlinear mixed-effects models under heavy-tailed distributions[J]. Pharmaceutical Statistics 2014, 13:81-93.
[2] Ramsay J O, and Silverman B W.函数型数据分析[M](第二版影印版).科学出版社,北京,2006.
[3] Ferraty F, and Vieu P. Nonparametric Functional Data Analysis:Theory and Practice[M].Springer New York USA, 2006.
[4] Koenker R, and Bassett G. JR. Regression quantiles[J]. Econometrica, 1978, 46:33-50.
[5] Cardot H, Crambes C, and Sarda P. Quantile regression when the covariates are functions[J].Journal of Nonparametric Statistics, 2005, 17:841-856.
[6] Ferraty F, Rabhi A, and Vieu P. Conditional quantiles for dependent functional data with application to the climatic El Nino phenomenon[J]. Sankhya, 2005, 67:378-398.
[7] Kato K. Estimation in functional linear quantile regression[J]. The Annals of Statistics, 2012,40(6):3108-3136.
[8] Lu Y, Du J, and Sun Z. Functional partially linear quantile regression model[J]. Metrika, 2014,77:317-332.
[9] Tang Q, and Kong L. Quantile regression in functional linear semiparametric model[J]. Statistics,2017, 51(6):1342-1358.
[10] Zhou J, Du J, and Sun Z. M-estimation for partially functional linear regression model based on splines[J]. Communications in Statistics, 2015, 45(21):6436-6446.
[11] Boente G, and Vahnovan A. Robust estimators in semi-functional partial linear regression models[J]. Journal of Multivariate Analysis, 2017, 154:59-84.
[12] Andrews D F, and Mallows C L. Scale mixtures of normal distributions[J]. Journal of the Royal Statistical Society, Series B, 1974, 36:99-102.
[13] Liu C. Bayesian robust multivariate linear regression with incomplete data[J]. Journal of the American Statistical Association, 1996, 91:1219-1227.
[14] Lange K, and Sinsheimer J. Normal/independent distributions and their applications in robust regression[J]. Journal of Computational and Graphical Statistics, 1993, 2:175-198.
[15] Choy S T B, and Smith A F M. Hierarchical models with scale mixtures of normal distributions[J]. Test, 1997, 6:205-221.
[16] Rosa G J M, Gianola D, and Padovani C R. Bayesian longitudinal data analysis with mixed models and thick-tailed distributions using MCMC[J]. Journal of Applied Statistics 2004, 31:855-873.
[17] Meza C, Osorio F, and la Cruz R D. Estimation in nonlinear mixed-effects models using heavytailed distributions[J]. Statistics and Computing 2012, 22:121-139.
[18] De la Cruza R. Bayesian analysis for nonlinear mixed-effects models under heavy-tailed distributions[J]. Pharmaceutical Statistics 2014, 13:81-93.