An Information - Theoretic Approach to the Measurement Error Model

• Autorzy: Amjad D. Al-Nasser
• Języki publikacji: EN

Abstrakty

EN

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. (original abstract)

Słowa kluczowe

EN

Entropy; Estimation; Maximum likelihood estimation; Estimation theory

PL

Entropia; Estymacja; Metoda największej wiarygodności; Teoria estymacji

• Czasopismo: Statistics in Transition
• Rocznik: 2010
• Tom: 11
• Numer: nr 1
• Strony: 9--24

Twórcy

autor

Amjad D. Al-Nasser

Bibliografia

• 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 StatisticalMethods.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, 2351.
• 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.