Ridge estimation in linear mixed measurement error models with stochastic linear mixed restrictions. Issue 6 (3rd June 2022)

• Record Type: Journal Article
• Authors: Yavarizadeh, Bahareh; Rasekh, Abdolrahman; Ahmed, Syed Ejaz; Babadi, Babak
• Is Part Of: Communications in statistics. Volume 51:Issue 6(2022)
• Page Start: 3037
• Page End: 3053
• Publication Date: 2022-06-03
• Subjects: Measurement error -- Multicollinearity -- Ridge estimation -- Stochastic restricted ridge estimation; 62J05 -- 62J07; Mathematical statistics -- Periodicals; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5
• DOI: 10.1080/03610918.2019.1705974
• Languages: English
• ISSNs: 0361-0918

Abstract

Abstract: This article is concentrated on the problem of multicollinearity in linear mixed models (LMMs) with measurement error in the fixed effects variables. After introducing a ridge estimator (RE) in these models, we propose a new estimator called the stochastic restricted ridge estimator (SRRE) by combining the ridge estimator (RE) and the stochastic restricted estimator (SRE). Moreover, asymptotic properties of these estimators will be derived and the necessary and sufficient conditions for the superiority of the SRRE over the RE and SRE are obtained using the mean squared error matrix (MSEM). Finally, the theoretical findings of the proposed estimators are also evaluated with a Monte Carlo simulation study and a numerical example.