| 具有高斯过程误差的函数型线性模型的统计诊断 |
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| 引用本文： | 陈刚,黄超,林金官.具有高斯过程误差的函数型线性模型的统计诊断[J].应用数学与计算数学学报,2014(1):117-126. |
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| 作者姓名： | 陈刚 黄超 林金官 |
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| 作者单位： | 南通职业大学基础课部;东南大学数学系 |
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| 基金项目： | supported by the National Natural Science Foundation of China(11171065);the National Natural Science Foundation of Jiangsu Province of China(BK2011058);the Fund for the Doctoral Program of Higher Education of China(20120092110021) |
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| 摘 要： | 提出了具有高斯过程误差的函数型回归模型的几种诊断方法.在此模型中,首先,在样条基的基础上,推导了回归系数函数的估计.随后,证明了数据删失模型和均值漂移模型的等价性.然后,研究了三种诊断方法,即残差分析、Cook距离和似然距离来诊断异常和强影响数据.最后,通过一个模拟例子和一个实例来阐述方法的有效性.
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| 关 键 词： | 函数型线性回归 样条基 残差 Cook距离 似然距离 |
Statistical diagnostics for functional linear regression models with Gaussian process errors |
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| CHEN Gang;HUANG Chao;LIN Jin-guan.Statistical diagnostics for functional linear regression models with Gaussian process errors[J].Communication on Applied Mathematics and Computation,2014(1):117-126. |
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| Authors: | CHEN Gang;HUANG Chao;LIN Jin-guan |
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| Institution: | CHEN Gang;HUANG Chao;LIN Jin-guan;Department of Basic Courses,Nantong Vocational University;Department of Mathematics,Southeast University; |
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| Abstract: | Several diagnostic measures are proposed in functional linear regression models with Gaussian process errors.The estimators of unknown regression coefficient functions are first derived based on the spline basis.Then,it is proved that the case-deletion model is equivalent to the mean-shift outlier model.Three diagnostic methods are presented,which are the residual analysis,Cook＇s distance,and the likelihood distance to check outliers and influential cases,and illustrated by a simulated example and a real data example. |
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| Keywords: | functional linear regression spline basis residual Cook＇s distance likelihood distance |
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