Least Orthogonal Distance Estimator and Total Least Square

Naccarato, Alessia and Zurlo, Davide and Pieraccini, Luciano (2012): Least Orthogonal Distance Estimator and Total Least Square.

Abstract

Least Orthogonal Distance Estimator (LODE) of Simultaneous Equation Models’ structural parameters is based on minimizing the orthogonal distance between Reduced Form (RF) and the Structural Form (SF) parameters. In this work we propose a new version – with respect to Pieraccini and Naccarato (2008) – of Full Information (FI) LODE based on decomposition of a new structure of the variance-covariance matrix using Singular Value Decomposition (SVD) instead of Spectral Decomposition (SD). In this context Total Least Square is applied. A simulation experiment to compare the performances of the new version of FI LODE with respect to Three Stage Least Square (3SLS) and Full Information Maximum Likelihood (FIML) is presented. Finally a comparison between the FI LODE new and old version together with few words of conclusion conclude the paper.

• Item Type: MPRA Paper
• Language: English
• Keywords: Least Orthogonal Distance Estimator, Simultaneous Equation Models, Total Least Square
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation

References

T. W. ANDERSON, (1976), Estimation of linear functional relationship: approximate distribution and connections with simultaneous equation in econometrics, Journal of the Royal Statistics Society, Ser. B, 38, pp. 1-20.

J. G. CRAGG, (1967), On Relative Small Sample Properties of Several Structural Equation Estimator, Econometrica, vol. 35.

C. ECKART, G. YOUNG, (1936), The approximation of one matrix by another of lower rank, Psychometrika, Vol. 1, No. 3.

L.GLESER, (1981), Estimation in a multivariate “errors in variable model” regression model : Large sample results, Ann. Statistics, Vol. 9, pp. 525-534.

G. H. GOLUB, C. VAN LOAN, (1980), An analysis of the total least square problem, SIAM J., Number Anal. 17.

L. S. JENNINGS, (1980), Simultaneous Equation Estimation computational aspects, Journal of Econometrics, Vol. 12, pp. 23-39.

T. C. KOOPMANS, H. RUBIN, R. B. LEIPNIK, (1950), Measuring the Equation System of Dynamic Economics, In: Statistical Inference in Dynamic Economic Models, T. C. Koopmans Ed., New York John Wiley & Sons, Inc., Chapter 2, pp. 53-237.

I. MARKOVSKY, S. VAN HUFFEL, (2007), Overview on total least square, Signal Processing, Vol. 87, pp. 2283-2303.

A. NACCARATO, D. ZURLO, (2008), A Monte Carlo Study on Full Information Methods in Simultaneous Equation Models, Quaderni di Statistica, Vol. 10, pp. 115-144.

L. PIERACCINI, A. NACCARATO, (2008), Full information Least Orthogonal Distance Estimator of Structural Parameters in Simultaneous Equation Models, Statistica, Vol. spec., pp. 52-76.

L. PIERACCINI, (1988), Il metodo L.O.D.E. per la stima dei parametri strutturali di un sistema di equazioni simultanee, Quaderni di statistica e Econometria, Vol. X, pp. 5-14.

L. PIERACCINI, (1983), The Estimation of Structural Parameters in Simultaneous Equation Models, Quaderni di statistica e Econometria, Vol. V, pp. 1-21.

L. PIERACCINI, (1969), Su un’interpretazione alternativa del metodo dei minimi quadrati a due stadi, Statistica, Vol. 4 XI, pp. 786-802.

H. THEIL, A. ZELLNER, (1962), Three stage least squares: simultaneous estimation of simultaneous equation, Econometrica, Vol. 30.

S. VAN HUFFEL, (2007), Total least square and error in variable model, Computational Statistics and Data Analysis, Vol. 52, pp. 1076-1079.

S. VAN HUFFEL, (2002), Total Least Squares and Errors-In-Variables Modeling: Analysis, Algorithms and Applications, Kluwer Academic Publications.

S. VAN HUFFEL, (1989), The partial total least square algorithm, J. Computational Analysis, Vol. 93, pp. 149-162.

S. VAN HUFFEL, (1988), Analysis an properties of the generalized total least square problem, SIAM J., Matrix Anal. Appl., Vol. 10, pp. 294-315.