A new ridge-type estimator in stochastic restricted linear regression

Local Influence Analysis for The Ridge Regression Under Stochastic Linear Restrictions

“…Under such stochastic restrictions, the influential results are comparable to previous articles (Shi, 1999). However, when we use the influential observations (such as 4 and 10, which were found to be influential cases in those papers, by various approaches) or a general matrix (such as Li and Yang, 2011) as the stochastic restrictions, we find that the results are different from those obtained above and change with the stochastic restrictions we add. This is consistent with our common sense that the influential analysis depends on the stochastic restrictions, which again depends on the priori information available and justifies the necessity of taking into account the stochastic restrictions.…”

On the Weighted Mixed Almost Unbiased Ridge Estimator in Stochastic Restricted Linear Regression

“…In order to verify our theoretical results, we firstly conduct an experiment based on a real data set originally due to Woods et al [21]. In this experiment, we replace the unknown parameters and 2 by their unbiased estimators, which is according to the way in [17]. The result here and below is performed with R 2.14.1.…”

“…When the prior information and the sample information are not equally important, Schaffrin and Toutenburg [16] studied the weighted mixed regression and developed the weighted mixed estimator (WME). Li and Yang [17] grafted the RE into the weighted mixed estimation procedure and proposed the weighted mixed ridge estimator (WMRE).…”

Singular Ridge Regression With Stochastic Constraints

“…The ridge regression approach has been studied by Hoerl and Kennard (1970), McDonald and Galarneau (1975), Gibbons (1981), Saleh and Kibria (1993), Liu (1993Liu ( , 2003, Akdeniz and Kaciranlar (1995), Kaciranlar et al (1999Kaciranlar et al ( , 2011, Akdeniz and Erol (2003), Downloaded by [University of Otago] at 19:32 29 July 2015 Kibria (2003), Kibria and Saleh (2004), Zhong and Yang (2007), Xu (2009), Yang et al (2009), Akdeniz and Akdeniz Duran (2010), Mansson et al (2010), Li and Yang (2011), and Akdeniz Duran and Akdeniz (2012) to mention a few.…”