加权半参数模型及其应用效果分析
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摘要
提出一种加权半参数模型,对半参数模型中的参数分量与非参数分量分别加权,针对数据的不同特点合理确定权重。分别对模拟数据和GPS真实数据进行处理,并与最小二乘法、岭估计法和半参数模型进行对比,通过残差、均方误差等指标的对比分析可见,加权半参数估计模型得到的估计值与真值最接近,估计残差浮动平缓,均方误差小。
A weighted semi-parametric estimate model was presented. In the model,parameter components and non-parameter components are weighted respectively according to different characters of data. Simulated data and GPS data are both processed with the model. The results of comparation with least square estimation,ridge estimation and semi-parametric estimation and residual and mean square error indicate that the estimated values with weighted semi-parametric model approach the true values,the fluctuation of estimated residual is smoothest,and the mean square error is minimum.
A weighted semi-parametric estimate model was presented. In the model,parameter components and non-parameter components are weighted respectively according to different characters of data. Simulated data and GPS data are both processed with the model. The results of comparation with least square estimation,ridge estimation and semi-parametric estimation and residual and mean square error indicate that the estimated values with weighted semi-parametric model approach the true values,the fluctuation of estimated residual is smoothest,and the mean square error is minimum.
引文
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10 潘雄.半参数模型的估计理论及其应用[D].武汉:武汉大学,2005.(Pan Xiong.The estimation theory and application study on semi-parametric model[D].Wuhan:Wuhan University,2005)
11 赵春茹.半参数核估计理论及其在变形监测中的应用研究[D].武汉:中国地质大学,2011.(Zhao Chunru.Semiparametric kernel estimation theory and its application to deformation monitoring[D].Wuhan:China University of Geosciences,2011)
12 丁士俊.半参数回归模型核光滑估计及模拟计算分析[J].测绘通报,2010(3):1-3.(Ding Shijun.Kernel smoothing estimation of nonparametric model and simulated analysis[J].Bulletin of Surveying and Mapping,2010(3):1-3)
13 Langford J.Learning theory[M].Springer Berlin Heidelberg,2005.
14 Wong W.On the consistency of cross-validation in kernel nonparametric regression[J].The Annals of Statistics,1982,11(4):1 136-1 141.
15 黄海兰,牛犇.岭参数确定的研究[J].测绘科学,2011,36 (4):31-32.(Huang Hailan and Niu Ben.Study on ridge parameter determination[J].Science of Surveying and Mapping,2011,36(4):31-32)
16 Haber E and Oldenburg D.A GCV based method for nonlinear ill-posed problems[J].Computational Geosciences,2000(1):41-63.
17 王振杰,欧吉坤.用L-曲线法确定岭估计中的岭参数[J].武汉大学学报:信息科学版,2004,29(3):235-238 .(Wang Zhenjie and Ou Jikun.Determining the ridge parameter in a ridge estimation using L-curve method[J].Geomatics and Information Science of Wuhan University,2004,29(3):235-238)
2 Ruppert D.Wand M P and Carroll R J.Semiparametric regression[M].Cambridge:Cambridge University Press,2003.
3 王新洲.非线性模型参数估计理论与应用[M].武汉:武汉大学出版社,2002.(Wang Xinzhou.Theory and application of parameter estimation of nonlinear model[M].Wuhan:Wuhan University Press,2002)
4 Green P J and Sliverman B W.Nonparametric regression and generalized linear models[M].London:Chapman and Hall,1994.
5 Gao J T and Anh V V.Semiparametric regression under long-range dependent errors[J].J of Statistical Planning and Inference.1999,80(1-2):37-57.
6 Hardle W and Manmmen E.Testing parametric versus semiparametric modeling in generalized linear models[J].Journal of the American Statistical Association,1998,93:1 461-1 474.
7 洪圣岩.一类半参数回归模型的估计理论[J].中国科学(A辑),1999(12):1 258-1 272.(Hong Shengyan.A kind of semiparametric regression model estimation theory[J].Science in China(Ser.A),1999(12):1 258-1 272)
8 丁士俊.测量数据的建模与半参数估计[D].武汉:武汉大学,2005.(Ding Shijun.Survey data modeling and semiparametric estimating[D].Wuhan:Wuhan University,2005)
9 张松林.非线性半参数模型最小二乘估计理论及应用研究[D].武汉:武汉大学,2003.(Zhang Songlin.The theoretical and application study on nonlinear semiparametric model[D].Wuhan:Wuhan University,2003)
10 潘雄.半参数模型的估计理论及其应用[D].武汉:武汉大学,2005.(Pan Xiong.The estimation theory and application study on semi-parametric model[D].Wuhan:Wuhan University,2005)
11 赵春茹.半参数核估计理论及其在变形监测中的应用研究[D].武汉:中国地质大学,2011.(Zhao Chunru.Semiparametric kernel estimation theory and its application to deformation monitoring[D].Wuhan:China University of Geosciences,2011)
12 丁士俊.半参数回归模型核光滑估计及模拟计算分析[J].测绘通报,2010(3):1-3.(Ding Shijun.Kernel smoothing estimation of nonparametric model and simulated analysis[J].Bulletin of Surveying and Mapping,2010(3):1-3)
13 Langford J.Learning theory[M].Springer Berlin Heidelberg,2005.
14 Wong W.On the consistency of cross-validation in kernel nonparametric regression[J].The Annals of Statistics,1982,11(4):1 136-1 141.
15 黄海兰,牛犇.岭参数确定的研究[J].测绘科学,2011,36 (4):31-32.(Huang Hailan and Niu Ben.Study on ridge parameter determination[J].Science of Surveying and Mapping,2011,36(4):31-32)
16 Haber E and Oldenburg D.A GCV based method for nonlinear ill-posed problems[J].Computational Geosciences,2000(1):41-63.
17 王振杰,欧吉坤.用L-曲线法确定岭估计中的岭参数[J].武汉大学学报:信息科学版,2004,29(3):235-238 .(Wang Zhenjie and Ou Jikun.Determining the ridge parameter in a ridge estimation using L-curve method[J].Geomatics and Information Science of Wuhan University,2004,29(3):235-238)