Multiple singular values correction estimation based on signal-to-noise ratio

摘要：

针对线性模型的复共线性问题,提出了基于信噪比度量的多奇异值修正估计.复共线性对模型中各个参数的危害是有差异的,用信噪比估值可将其度量,以此将参数按危害程度的不同进行分类,同时得到对应设计矩阵的复共线性对参数估计危害的机理.以此为据,结合OR估计及TSVD估计的思想,提出了新算法MSVC估计.论证了MSVC估计是对TSVD估计和OR估计形式的统一.比较了MSVC估计、LS估计和OR估计各自的特点.MS-VC估计的优势在于,与LS估计相比,其偏差略有增加,换取方差较大下降;与OR估计相比,其方差略有增加,换取偏差较大下降.通过数值试验,表明了MSVC估计的解算精度较高.

Backward uncertain differential equaion is a special kind of differential equations driven by the Liu process. It studies the issue of how 1o make decisions and talke behavioral paths at the current moment in order to achieve the expected goals in the future under uncertain environment, Firstly, the relevant theory of backward uncertain differential equations is in-troduced and the solution of linear backward uncertain differential equation is given, Secondly, considering that the theory of backward uncertain differental cquation is sutable for investmont in fnancial market, an uncertain portfolio modd characterized by linear backward uncertain differential equation is established.

作者:

顾勇为,李新娜,郭淑妹,李国重,刘长健

Gu Yongwei，Li Xinna，Guo Shumei，Li Guozhong，Liu Changjianb

机构地区：

信息工程大学 a.基础部；b.地理空间信息学院

引用本文：

顾勇为,李新娜,郭淑妹等.基于信噪比度量的多奇异值修正估计[J].河南师范大学学报(自然科学版),2026,54(1):62-67.(Gu Yongwei, Li Xinna, Guo Shumei,et al.Multiple singular values correction estimation based on signal-to-noise ratio[J].Journal of Henan Normal University(Natural Science Edition),2026,54(1):62-67.DOI:10.16366/j.cnki.1000-2367.2024.07.08.0001.)

基金：

黑龙江省省属高等学校基本科研业务费国自然培育一般项目

关键词：

信噪比；复共线性；岭估计；奇异值；多参数

linear backward uncertain differential equations; Liu process; portfolio model

分类号：

P207

基于信噪比度量的多奇异值修正估计.pdf