[1]陆建.PC准则下生长曲线模型回归系数阵的一类线性估计的优良性[J].东南大学学报(自然科学版),2005,35(6):975-979.[doi:10.3969/j.issn.1001-0505.2005.06.032]
 Lu Jian.Superiority about a class of linear estimation of regression coefficient under Pitman Closeness criterion[J].Journal of Southeast University (Natural Science Edition),2005,35(6):975-979.[doi:10.3969/j.issn.1001-0505.2005.06.032]
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PC准则下生长曲线模型回归系数阵的一类线性估计的优良性()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
35
期数:
2005年第6期
页码:
975-979
栏目:
数学、物理学、力学
出版日期:
2005-11-20

文章信息/Info

Title:
Superiority about a class of linear estimation of regression coefficient under Pitman Closeness criterion
作者:
陆建
东南大学数学系, 南京 210096
Author(s):
Lu Jian
Department of Mathematics, Southeast University, Nanjing 210096, China
关键词:
Pitman Closeness准则 生长曲线模型 线性估计 最小二乘解
Keywords:
Pitman Closeness criterion growth curve model linear estimation the least squares solution
分类号:
O212.4
DOI:
10.3969/j.issn.1001-0505.2005.06.032
摘要:
设生长曲线模型为 Yn&#215;p=An&#215;mBm&#215;kCk&#215;p+En&#215;p,E~N(21521521521521502InIp).2当ATAT为病态时,令回归系数阵的最小二乘(LS)解和一类线性估计分别为(^overB)=(ATA)<sup>-ATYCT(CCT)-1TTTT1和(^overB)1=(ATA+ρΣ)-1ATYCT(CCT)-1,1T1TTT1其中ρ>0为常数为正定阵.分别在ATAT和Σ的可交换性未知和已知的情形下证明了:在适当条件下(^overB)11于PC准则下优于(^overB).并将这一结论推广到当ATAT和CCTT都是病态时的情况.
Abstract:
Let the growth curve model be Yn&#215;p=An&#215;mBm&#215;kCk&#215;p+En&#215;p,E~N(21521521521521502InIp2). Suppose that the least squares(LS)solution and linear estimation of regression coefficient are (^overB)=(ATA)<sup>-ATYCT(CCTTTTT)-1 and (^overB)1=(ATA+ρΣ)-1 ATYCT(CCT1T1TTT)-1,when ATAT is ill-conditioned,where ρ is a positive constant,Σ is a positive definite matrix. On the condition of exchangeability or unexchangeability of ATAT and Σ, it is proved that under suitable conditions the linear estimator (^overB)11 is better than (^overB) by Pitman Closeness criterion. This conclusion is then extended to the situation when ATAT and Σ are both ill-conditioned.

参考文献/References:

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备注/Memo

备注/Memo:
作者简介: 陆建(1980—),男,硕士生,luyilang@sohu.com.
更新日期/Last Update: 2005-11-20