COMPARISONS OF SOME BIASED ESTIMATORS FOR LINEAR MEASUREMENT ERROR MODELS
Abstract
Measurement errors are very often come upon in data analysis. Classical statistical methods become disadvantageous and ordinary least squares estimator of parameters turns into inconsistent and biased, in the existence of measurement errors in the data. Although some methods are used, the performances of them are not good enough in the presence of multicollinearity and measurement errors in the data, simultaneously. That’s why researchers have been inquiring about the estimation of the parameters if the measurement error models have multicollinearity, lately. Especially, biased estimation techniques have been researched in the existence of multicollinearity for measurement error models recently. In this paper, the ridge and Liu estimation approaches to the measurement error models in the existence of multicollinearity are investigated. The comparisons of the biased estimators’ performances are analyzed theoretically and numerically.
Keywords
Measurement Error Models, Reliability Matrix, Ridge Estimator, Liu Estimator,
References
- [1] Gleser LJ. The importance of assessing measurement reliability in multivariate regression, Journal of the American Statistical Association 1992; 87 (419): 696-707.
- [2] Cheng CL, Van Ness JW. Statistical Regression with Measurement Error, Arnold, London, 1999.
- [3] Fuller WA. Measurement Error Models. New York: Wiley, 1987.
- [4] Hoerl AE. Kennard RW. Ridge regression: Biased estimation for non-orthogonal Problems, Technometrics 1970; 12: 55-67.
- [5] Liu K. A new class of biased estimate in linear regression, Commun. Statist. Theor. Meth. 1993; 22: 393-402.
- [6] Saleh A.K.M.D. Shalabh, A ridge regression estimation approach to the measurement error model, Journal of Multivariate Analysis 2014; 123: 68-84.
- [7] Üstündağ Şiray G. Liu estimation approach to the measurement error models. Journal of Statistical Computation and Simulation 2019; 89(18): 3453-3496.
- [8] McDonald GC, Galarneau DI. A. Monte Carlo evaluation of some ridge-type estimators, J. Amer. Statist. Assoc. 1975; 20: 407-416.
- [9] Longley JW. An appraisal of least squares programs for the electronic computer from the point of view of the user. Journal of the American Statistical Association 1967; 62: 819-841.
- [10] Beaton AE, Rubin DB and Barone JL. The Acceptability of Regression Solutions: Another look at Computational Accuracy. Journal of the American Statistical Association 1976; 71(353): 158-168.