约束线性回归模型系数的条件岭估计及其性质

发布时间：2017-12-31 22:03

本文关键词：约束线性回归模型系数的条件岭估计及其性质　出处：《吉林大学》2017年硕士论文　论文类型：学位论文

【摘要】：在数理统计问题的研究中,线性回归模型的参数估计一直是研究热点.随着统计理论的发展,人们发现最小二乘估计在处理复共线性问题上的不足,一些有偏估计慢慢成为研究的重点.对于不带约束条件的线性回归模型中参数的估计已经有比较系统的研究结论.本文则基于带有齐次约束条件的线性回归模型来研究参数估计。本文从约束线性回归模型入手,首先介绍了约束最小二乘估计.其次着重从有偏估计角度出发,给出了一些约束型的有偏估计,如条件岭估计、岭型Stein估计.并且重点研究了条件岭估计,讨论了学者给出的两种条件岭估计定义,证明了两种条件岭估计具有等价性.随后在均方误差下,讨论了约束岭型Stein估计与约束最小二乘估计的关系。
[Abstract]:In the study of mathematical and statistical problems in parameter estimation of linear regression model has been a hot research. With the development of statistical theory, people find that the least squares estimation problems when dealing with multicollinearity problems, some biased estimates gradually become the focus of the study. The conclusion has been systematically studied for model parameter estimation of linear belt about the return beam condition. This paper is based on the study of parameter estimation with linear homogeneous constrained regression model. This paper from the restricted linear regression model with constrained least squares estimation is introduced firstly. Secondly, mainly from the perspective of biased estimation, given some constraint biased estimation, such as conditional ridge estimation, ridge type Stein estimation. And focus on the conditional ridge estimation, discussed the definition of the two conditions given by Ling scholars estimate, proved that the two conditional ridge estimation is equivalent. Then, under the mean square error, the relationship between constrained ridge Stein estimation and constrained least square estimation is discussed.

【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224

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