Consistent estimation of a regression with errors in the variables

Schneeweiß, Hans

doi:10.1007/bf01902854

Cited by 69 publications

(35 citation statements)

References 10 publications

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“…Further, we assume that u, V, and W are stochastically independent. These specifications can be relaxed at the cost of slight algebraic complexity but without any conceptual difficulty; see, e.g., Schneeweiss (1976). Thus, we have…”

Section: Model Specificationmentioning

confidence: 98%

“…The expression (4.16) in the special case of functional model has been obtained by Schneeweiss (1976).…”

Section: Using These In (34) Writingmentioning

confidence: 99%

“…One such popular approach involves the specification of the variance covariance matrix of measurement errors of the regressors. Utilizing it to overcome the problem of inconsistency in the context of functional variant of the model, Schneeweiss (1976) has presented the adjusted or corrected least squares estimator. He has demonstrated that the estimator is consistent.…”

Section: Introductionmentioning

confidence: 99%

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Improved Estimation in Measurement Error Models Through Stein Rule Procedure

Shalabh

1998

Journal of Multivariate Analysis

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This paper examines the role of Stein estimation in a linear ultrastructural form of the measurement errors model. It is demonstrated that the application of Stein rule estimation to the matrix of true values of regressors leads to the overcoming of the inconsistency of the least squares procedure and yields consistent estimators of regression coefficients. A further application may improve the efficiency properties of the estimators of regression coefficients. It is observed that the proposed family of estimators under some constraint on the characterizing scalar dominates the conventional consistent estimator with respect to the criterion of asymptotic risk under a specific quadratic loss function. Then the problem of prediction of the values of the study variable within the sample is considered, and it is found that the predictors based on the proposed family of estimators are always more efficient than the predictors based on the conventional estimator according to asymptotic predictive mean squared error criterion, although both are biased. Academic PressAMS 1991 subject classifications: 62J07, 62F11.

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Section: Model Specificationmentioning

confidence: 98%

“…The expression (4.16) in the special case of functional model has been obtained by Schneeweiss (1976).…”

Section: Using These In (34) Writingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Improved Estimation in Measurement Error Models Through Stein Rule Procedure

Shalabh

1998

Journal of Multivariate Analysis

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“…(16), that is, 17), which is a function of i and W. To obtain a consistent estimate, the corrected LS method, the socalled CLS estimate of a, is utilized [13]. For simplicity, here we assume 'r i W is a Gaussian white-noise distribution with a zero mean and a variance V 2 , and is statistically independent of r i W. The CLS estimate of a is then given by where N 2L 0 1.…”

Section: Model With Perturbation and Cls Estimate 41 Estimation Errmentioning

confidence: 99%

Detection of direction and number of impinging signals in array antennas using cyclostationarity

Tsuji

Xin

Yoshimoto

et al. 1999

Electron. Comm. Jpn. Pt. I

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“…In the case of multiple measurement error model, the additional information in the form of known covariance matrix of measurement errors associated with explanatory variables and known reliability matrix of explanatory variables are the two popular forms which provide the consistent estimate of regression coefficient vector, see, e.g. Cheng and Van Ness (1991), Schneeweiss (1976), Gleser (1992Gleser ( , 1993, Shalabh (2003) etc. Our modest objective in this paper is to use both types of available information and obtain an appropriate coefficient of determination which can be used to judge the goodness of fit of a measurement error model.…”

Section: Introductionmentioning

confidence: 99%

Coefficient of determination for multiple measurement error models

Cheng

Shalabh

Garg

2014

Journal of Multivariate Analysis

102

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The coefficient of determination (R 2 ) is used for judging the goodness of fit in a linear regression model. It gives valid results only when the observations are correctly observed without any measurement error. The R 2 provides invalid results in the presence of measurement errors in the data in the sense that sample R 2 becomes an inconsistent estimator of population multiple correlation coefficient between the study variable and explanatory variables. The corresponding variants of R 2 which can be used to judge the goodness of fit in multivariate measurement error model have been proposed in this paper. These variants are based on the utilization of information on known covariance matrix of measurement errors and known reliability matrix associated with explanatory variables. The asymptotic properties of the traditional R 2 and proposed R 2 have been studied.

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Consistent estimation of a regression with errors in the variables

Cited by 69 publications

References 10 publications

Improved Estimation in Measurement Error Models Through Stein Rule Procedure

Improved Estimation in Measurement Error Models Through Stein Rule Procedure

Detection of direction and number of impinging signals in array antennas using cyclostationarity

Coefficient of determination for multiple measurement error models

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