K - Class estimators - a Review

Zoha Qayyum; S. Suhaib Hasan

doi:https://doi.org/10.14445/22315373/IJMTT-V50P515

International Journal of Mathematics Trends and Technology

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Volume 50 | Number 2 | Year 2017 | Article Id. IJMTT-V50P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V50P515

K - Class estimators - a Review

Zoha Qayyum, S. Suhaib Hasan

Abstract

In the estimation of linear equations various estimators have been developed over the years. An important family of estimators which includes many interesting estimators is K-class estimators based on the pioneering work of Previous researchers. In this paper an attempt has been made to review the work done on the properties of K-class estimators, both asymptotic and small sample properties. The case of small disturbances and system estimators has also been covered. In the end scope for their investigations is briefly discussed.

Keywords

Estimation, Econometric relation, Least Squares, Asymptotic and small sample, Small disturbance.

References

[1] A.R Bergstrom, “The Exact Sampling Distributions of Least Squares and Maximum Likelihood Estimators of the Marginal Propensity to Consume.” Econometrica, 30 pp. 480-490, 1962.
[2] A. S. Goldberger. An instrumental variable interpretation of k-class estimation. Indian Economic Journal, 13(3), 424, 1965.
[3] A. L. Nagar, “The Bias and the Moment Matrix of the General k-class Estimators of Parameters in Simultaneous Equations.” Econometrica, 27 (October), pp. 575-595, 1959.
[4] A. L. Nagar “A Monte-Carlo Study of Alternative Simultaneous Equations Estimators.” Econometrica, (July) pp. 573-590, 1960.
[5] A. L. Nagar, “A Note on the Residual Variance Estimation in Simultaneous Equations.” Econometrica, 29, pp. 238-24, 1961.
[6] A. Maeshiro, “A Simple Mathematical Relationship Among k-class Estimators.” Journal of the American Statistical Association, Vol.61, 368-374, 1966.
[7] D. G. Kabe.“A Note on the Exact Distributions of Generalized Classical Least Squares Estimators in Two Leading Over-Identified Cases.” Journal of the American Statistical Association, 58, 535-537, 1963.
[8] D. G. Kabe. “A Note on the Exact Distributions of Generalized Classical Least Squares Estimators in Leading Three Equation Case.” Journal of the American Statistical Association, 59, 881-894, 1964.
[9] D. H. Richardson, “On the Distribution of the Identifiability Test Statistic.” In Papers in Quantitative Economics, ed by J.P.Quirk and Lawrence: The University Press of Kansas. 1968.
[10] G.F Brown, J.G. Ramage and V.K.Srivastava. Disturbances-Variance Estimation in Simultaneous Equation, Systems Journals of Quantitative Economics, Vol.1 pp.231-251, 1985.
[11] H. Theil, “Economic Forecasts and Policy.” (2nd ed.), Amsterdam: North Holland publishing co, 1961.
[12] H. Theil, “Principles of Econometrics.” New York: John Wiley and Sons, 1971.
[13] J. G. Cragg, “On the Relative Small-Sample Properties of Several Structural-Equation Estimators.” Econometrica, Vol.35, No.1, 1967.
[14] J.B Kadane, “Comparison of -class Estimators When the Disturbances are Small.” Econometrica, 39, 723-737, 1971.
[15] J. M. Lord Keynes. “General Theory of Employment, Interest and Money.” London, 1936.
[16] K. Takeuchi, “Exact Sampling moments of the Ordinary Least Squares, Instrumental Variables and Two-Stage Least Squares Estimators.” International Economic Review, 11, 1-12, 1970.
[17] K. R. Kadiyala, “An Exact Small Sample Property of the k-class Estimators”, Econometrica, 36, 930-932, 1970.
[18] R.E. Quandt,. “On Certain Small Sample Properties of k-class Estimators.” International Economic Review, Vol 6, No. 1. January, 1965.
[19] R.L Basmann. “A Note on the Exact Finite Sample Frequency Functions of Generalized Classical Linear Estimators in a Leading Three Equation Case.” Journal of the American Statistical Association, Vol 58, pp. 161-6171, 1963a.
[20] R.L Basmann. “Remarks Concerning the Application of Exact Finite Sample Distribution Functions of GCL Estimators in Econometric Statistical Inference.” Journal of the American Statistical Association, Vol 58, pp. 943-976, 1963b.
[21] R.L Basmann. “A Note on the Exact Finite Sample Frequency Functions of Generalized Classical Linear Estimators in Two Leading Over-Identified Cases.” Journal of the American Statistical Association, Vol 56, pp. 619-636, 1961.
[22] R. S. Mariano “On Distributions and Moments of Single-Equation Estimators in a Set of Simultaneous Linear Stochastic Equations.” Technical Report no. 27, Institute of Mathematical Studies in the Social Sciences, Standard Ford University, 1969.
[23] T. Sawa, “The Exact Sampling Distributions of Ordinary Least Squares and Two-Stage Least Squares Estimators.” Journal of the American Statistical Association, 64, 923-937, 1968.
[24] T. Sawa, “Exact Finite Sampling Distribution of the LIML.” Discussion Paper Series No, 20, Kyoto Institute of Economic Research, Kyoto University, 1969.
[25] T. Sawa, “Finite Sample Properties of the k-class Estimators.” Econometrica, 40, No 4, pp. 653-680, 1972.
[26] T. N. Srinivasan, Approximations to the Finite Sample Moments of Estimators whose Exact Sampling Distributions are Unknown.” Econometrica, 38, pp. 533-541, 1970.
[27] T.W Anderson and Takamitsu Sawa. “Distributions of Estimates of Coefficients of a Single Equation in a Simultaneous System and their Asymptotic Expansions.” Econometrica, Vol. 41, No. 4, 1973.
[28] V.K. Srivastava, “Disturbance-Variance Estimation in Simultaneous Equations when Disturbances are Small.” Journal of American Statistical Association, Vol 67, No. 337, 1972.
[29] V.K. Srivastava, “Disturbance Variance Estimator.” Sankhya, Series C, Vol, 39 pp. 99-102, 1978.
[30] V.K. Srivastva and Ramji Tiwari (1976). “Two-stage and Three Stage Least Squares Estimation of Dispersion Matrix of Disturbance in Simultaneous Equations.” Annals of the Institute of Statistical Mathematics, Vol, 28 pp 411-428.
[31] V. K. Srivastava and Ramji Tiwari, “A Simple Derivation of the Identity Connecting Double k-class and Two-Stage Least Squares Estimators.” Sankhya, Series C, Vol.39, pp. 1-2, 1977.
[32] V. K. Srivastava and Ramji Tiwari, “Efficiency of Two-Stage and Three Stage Least Squares Estimators.” Econometrica, Vol. 46, no 6 (November), 1978.
[33] V. K. Srivastava and A.K.Srivastava, “A Note on Moments of k-class Estimator for Negative k.” Journal of Econometrics. Vol. 21, pp. 257-260, 1983.
[34] Walter.Y Oi, “On the Relationship among Different Members of the k-Class.” International Economic Review. Vol.10, no. (1969), 36-46, 1969.

Citation :

Zoha Qayyum, S. Suhaib Hasan, "K - Class estimators - a Review," International Journal of Mathematics Trends and Technology (IJMTT), vol. 50, no. 2, pp. 104-107, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V50P515