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

doi:10.7523/j.issn.2095-6134.2012.2.001

›› 2012, Vol. ›› Issue (2): 145-153.DOI: 10.7523/j.issn.2095-6134.2012.2.001

• Research Articles • Next Articles

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 Online:2012-03-15
Supported by:
Supported by National Natural Science Foundation of China (10801133) and President Foundation of GUCAS

Abstract

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

CLC Number:

O212

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

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