The weighted ridge estimator in stochastic restricted linear measurement error models
type: Item
instance of: scholarly article
title: The weighted ridge estimator in stochastic restricted linear measurement error models
zbMATH Open document ID: 1408.62125
author: F. Ghapani
author: A. R. Rasekh
author: B. Babadi
published in: Statistical Papers
publication date: 2018-08-02T00:00:00Z
review text: The linear measurement error model \(y=Z\beta+\epsilon,~ X=Z+\Delta\) is considered, where \(y\) is a vector of response variables, \(Z\) is a matrix of unobservable values of regressors which can be observed through the matrix \(X\) with the measurement error \(\Delta,~ \beta\) is a vector of regression coefficients, and \(\epsilon\) is a vector of random errors. The covariance structure of the measurement errors is known, and the covariance matrix of \(\epsilon\) is known up to a scalar factor \(\sigma^2\). The vector \(\beta\) is subject to linear restrictions \(r=R\beta+e,\) where \(r\) is an observable random vector, \(R\) is a known matrix and \(e\) is an error vector, with covariance matrix known up to the scalar factor \(\sigma^2\). The random matrix \(\Delta\) and the random vectors \(\epsilon,~e\) are mutually independent. \textit{B. Schaffrin} and \textit{H. Toutenburg} [Z. Angew. Math. Mech. 70, No. 6, 735--738 (1990; Zbl 0714.62061)] developed the weighted mixed estimator (WME) by assigning not necessarily equal weights in the sample and prior information. In the paper under review, the weighted mixed ridge estimator (WMRE) is introduced. The performance of the WMRE against the WME is examined in terms of the asymptotic mean squared error matrix related to asymptotic normal distributions of the two estimators. A simulation study and a numerical example are given to illustrate the theoretical results.
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62J07
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 6912431
zbMATH Keywords: asymptotic mean squared error matrix
zbMATH Keywords: mixed ridge estimator
zbMATH Keywords: ridge estimator
zbMATH Keywords: weighted mixed estimator
zbMATH Keywords: weighted mixed ridge estimator
reviewed by: A. Kukush
MaRDI profile type: Publication
full work available at URL: s00362-016-0786-3
OpenAlex ID: W2419815693
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DOI: 10.1007/S00362-016-0786-3
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description: scientific article; zbMATH DE number 6912431