复值型数据Improper线性回归模型的估计

doi:10.7523/j.issn.2095-6134.2012.2.001

中国科学院大学学报 ›› 2012, Vol. ›› Issue (2): 145-153.DOI: 10.7523/j.issn.2095-6134.2012.2.001

• 数学与物理学 • 下一篇

复值型数据Improper线性回归模型的估计

闫长君¹, 张三国¹, 宁炜²

1. 中国科学院研究生院数学科学学院, 北京 100049;
2. 鲍灵格林州立大学数学与统计系, OH 43403 USA

收稿日期:2011-03-11 修回日期:2011-04-02 发布日期:2012-03-15
通讯作者: 张三国
基金资助:
Supported by National Natural Science Foundation of China (10801133) and President Foundation of GUCAS

Estimations of the improper linear regression models with complex-valued data

YAN Chang-Jun¹, ZHANG San-Guo¹, NING Wei²

1. Graduate University, Chinese Academy of Sciences, Beijing 100049, China;
2. Department of Mathematics and Statistics, Bowling Green State University, OH 43403, USA

Received:2011-03-11 Revised:2011-04-02 Published:2012-03-15
Supported by:
Supported by National Natural Science Foundation of China (10801133) and President Foundation of GUCAS

摘要/Abstract

摘要：

复随机变量称为"improper"随机变量,若它的"伪"协方差阵不为0,否则称为"proper"随机变量. 研究了误差服从独立同分布的improper复高斯分布的线性回归模型. 利用极大似然方法和2阶段最小二乘方法来估计回归系数. 模拟表明,这2种方法与经典复版本的最小二乘法有不同之处,并将该方法用于实际风信号数据的处理.

关键词: 复值型数据, improper, 复高斯分布

Abstract:

A complex-valued random variable is improper if its complementary covariance is not 0, otherwise it is proper. In this paper, we consider the linear regression models whose errors are independent and identically distributed following an improper complex Gaussian distribution. Such a model may be encountered in signal processing. We use the maximum likelihood method and the two-stage least squares method to estimate the regression coefficients. Differences between these two methods and the complex version of least squares estimates are investigated by simulations. A wind data set is used to illustrate the proposed approach.

Key words: complex-valued data, improper, complex Gaussian distribution

中图分类号:

O212

闫长君, 张三国, 宁炜. 复值型数据Improper线性回归模型的估计[J]. 中国科学院大学学报, 2012, (2): 145-153.

YAN Chang-Jun, ZHANG San-Guo, NING Wei. Estimations of the improper linear regression models with complex-valued data[J]. , 2012, (2): 145-153.

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复值型数据Improper线性回归模型的估计

Estimations of the improper linear regression models with complex-valued data

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