A new ridge estimator in linear measurement error model with stochastic linear restrictions

Abstract

Abstract. In this paper, a new ridge-type estimator is proposed and termed as the new mixed ridge estimator (NMRE) which is obtained by unifying the sample and prior information in linear measurement error model with additional stochastic linear restrictions. The new estimator is a generalization of the mixed estimator (ME) and ridge estimator (RE). The performances of this new estimator and mixed ridge estimator (MRE) with respect to the ME are examined under the criterion of mean squared error matrix. Finally, a numerical example and a Monte Carlo simulation are also presented to analyze.

Instrumental Variables Regression with Measurement Errors and Multicollinearity in Instruments

“…where ξ = n − 1 2 Φ T X is asymptotically normal with mean n − 1 2 Z T Zη (See for example, Fung et al ( 2003) and Ghapani and Babadi (2016)). So, we readily conclude that…”

“…Carrasco and Tchuente (2015) regularized versions of the limited information maximum likelihood (LIML). Also, Rasekh (2006), Ghapani and Babadi (2016) and Saleh, E., Shalabh (2014) presented the connection between measurement error models and ridge estimators. In this paper we employ the ridge regression method to combat multicollinearity in the estimation of IV models in the presence of some measurement errors.…”

Ridge stochastic restricted estimators in semiparametric linear measurement error models

“…In each group, there are different numbers of vessels from the same fabric code and provenance, which can essentially be regarded as replicated observations. Ghapani and Babadi (2016) and Rasekh (2001) analyzed the same data to find anomalous observations in full parametric linear measurement error models using the methods of shift outlier model and local influence approach, respectively. They considered Na measured with NAA as response variable versus mineral elements Na, Al,K, V, Cr and Mn measured by ICP as predictor variables.…”

“…To investigate the performance of the proposed stochastic restricted estimators, from previous studies (see, Ghapani and Babadi (2016)) we consider the parametric…”

“…The suggested idea is to use the ridge regression approach over the measurement error ridden data. In full-parametric linear measurement error models Rasekh (2001), Saleh (2014) and Ghapani and Babadi (2016) have considered collinearity in terms of a relationship between the elements of unobservable values and generalized ridge technique estimation to combat multicollinearity. However, there does not seem to be a work considering possible effects that collinearity can have on the different aspects of the estimates of parameters in semiparametric linear measurement error models (SLMeMs), nor to ridge estimation procedure as an alternative in the presence of collinearity and ill conditioning.…”