An information-theoretic approach to the measurement error model

Amjad D. Al-Nasser

doi:https://doi.org/10.59170/stattrans-2010-001

An information-theoretic approach to the measurement error model

Amjad D. Al-Nasser Statistics in Transition new series, vol. 11, 2010, 1, pages: 9-24 Published online: 1 July 2010 https://doi.org/10.59170/stattrans-2010-001

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ABSTRACT

In this paper, the idea of generalized maximum entropy estimation approach (Golan et al. 1996) is used to fit the general linear measurement error model. A Monte Carlo comparison is made with the classical maximum likelihood estimation (MLE) method. The results showed that, the GME is outperformed the MLE estimators in terms of mean squared error. A real data analysis is also presented.

KEYWORDS

Measurement Error Model, Generalized Maximum Entropy, Maximum Likelihood

REFERENCES

AL-NASSER, A. 2005. Entropy Type Estimator to Simple Linear Measurement Error Models. Austrian Journal of Statistics. 34(3). 283–294.

AL-NASSER, A. 2004. Estimation of Multiple Linear Functional Relationships. Journal of Modern Applied Statistical Methods.3 (1), 181–186.

AL-NASSER, A. 2003. Customer Satisfaction Measurement Models: Generalized Maximum Entropy Approach. Pakistan Journal of Statistics. 19(2), 213–226.

CARROLL, R. J., RUPPERT, D. and STEFANSKI, L. A. 1995. Measurement Error in Nonlinear Models. Chapman and Hall, London.

CHI-LUN CHENG and JOHN W. VAN NESS. 1999. Statistical Regression with Measurement Error. Arlond: N.Y: USA.

CSISZAR, I. 1991. Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems. The Annals of Statistics, 19, 2032–2066.

Department of Statistics. 2007. Statistical Yearbook, 58th Issue, Amman, Jordan.

DOLBY, G. R., 1976, The ultra-structural model: A synthesis of the functional and structural relations, Biometrika 63, 39–50.

DONHO, D. L, JOHNSTONE, I.M, HOCH, J.C, and STERN A.S 1992. Maximum entropy and nearly black object. J. Royal, Statistical Society, Ser B, 54, 41–81.

GOLAN, A. (2008). Information and Entropy Econometrics – A Review and Synthesis. Foundations and Trends in Econometrics. 2, 1–2, 1–145.

GOLAN, A. JUDGE, G. MILLER, D.1996. A maximum Entropy Econometrics: Robust Estimation with limited data, Wiley, New York.

GOLAN, A. JUDGE, G. PERLOFF, J. 1997. Estimation and Inference with Censored and Ordered Multinomial Response Data. J. Econometrics. 79, 23–51.

GLESER, L. J .1985. A note on G. R. Dolby’s unreplicated ultrastructural model. Biometrika, 72, 117–124.

JAYNES, E. T. 1957(a,b). Information and Statistical Mechanics (I, II). Physics Review (106,108), (620–630, 171–190).

QUIRINO PARIS. 2001. Multicollinearity and Maximum Entropy Estimators. Economics Bulletin. Vol.3, No.11, 1–9.

PEETERS, L. (2004). Estimating a random-coefficients sample-selection model using generalized maximum entropy. Economics Letters. 84: 87–92

PUKELSHEIM, F. 1994. The Three Sigma Rule. The American Statistician, Vol.48, no.2, 88–91. SRIVASTAVA, A. K, SHALABH. 1997. Consistent estimation for the nonnormal ultrastructural model, Statist. Probab. Lett. 34 .67–73.

SHANNON C, E. 1948. A Mathematical Theory of Communication. Bell System Technical Journal. 27, 379–423.