Abstract
A generalized mixed regression estimator for the estimation of the regression coefficients in the linear regression model with incomplete prior information is proposed and its properties are studied considering the risk under the general quadratic loss function when the disturbances are small and non normal.
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References
Goldstein M. and Smith A.F.M. (1974). Ridge type estimators for regression Analysis, JRSS B (36), 284–291.
Hocking R.R., Speed F.M. and Lynn M.J. (1976). A class of biased estimators in linear regression, Technometrics (18), 425–437.
Judge G.G., Griffiths N.E., Hill R.C. and Lee T.C. (1980). The Theory and Practice of Econometrics, John Wiley, New York.
Kadane J.B. (1971). Comparison of k-class estimators when the disturbances are small, Econometrica (39), 723–737.
Kakwani N.C. (1968). Note on the unbiasedness of a mixed regression estimator, Econometrica (36), 610–611.
Metha J.S. and Swamy P.A.V.B. (1970). The finite sample distribution of Theil’s mixed regression estimator and a related problem, International Statistical Review (38), 202–209.
Nagar A.L. and Kakwani N.C. (1964). The bias and moment matrix of a mixed regression estimator, Econometrica (32), 174–182.
Oehlert G.W. (1992). A note on the delta method, Amer. Statist. (46), 27–29.
Rao C.R. (1973). Linear Statistical Inference and its Applications, New York: John Wiely.
Singh R. Karan. (1994). Estimation of restricted regression model when disturbances are not necessarily normal, Statistics & Probability Letters (19), 101–109.
Singh R. Karan, Pandey S.K. and Srivastava V.K. (1994). A generalized class of shrinkage estimators in linear regression when disturbances are not normal, Commun. Statist.- Theory Math., 23(7).
Srivastava A.K. and Chandra R. (1991). Improved estimation of restricted resression model when disturbances are not necessarily normal, Sankhya, Ser. B(53), 119–133.
Srivastava V.K. and Chandra R. (1985). Properties of the mixed regression estimators when disturbances are not necessarily normal, Journal of Statistical Planning and Inference (11), 15–21.
Theil H. and Goldberger A.S. (1961). On pure and mixed statistical estimation in Economics, International Economic Review (2), 65–78.
Toutenburg H. (1975). The use of mixed prior information in regression analysis, Biom. Z. (17), 363–372.
Tracy D.S. and Srivastava A.K. (1988). A synthesis of Stein-rule and mixed regression procedures in linear regression models under non-normality, Commun. Statist.-Theory Meth. 17(3), 691–704.
Ullah A., Srivastava V.K. and Chandra R. (1983). Properties of shrinkage estimators in linear regression when disturbances are not normal, Journal of Econometrics (21), 389–402.
Vinod H.D. and Ullah A. (1981). Recent Advances in Regression Methods, New York: Marcel Dekker.
Zellner A. (1971). An Introduction to Bayesian Inference in Econometrics, John Wiely and Sons, Inc.
Zellner A. (1976). Bayesian and non-Bayesian analysis of the regression model with multivariate Student-t error terms, J. Amer. Statist. Assoc. (71), 400–405.
Zellner A. and Vandaele W. (1975). Bayes-Stein estimators for k-means, regression and simultaneous equations model, In studies in Bayesian Econometrics and Statistics, eds. S.E. Feinberg & A. Zellner, 627–653.
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Verma, S., Singh, R.K. A modified generalized mixed regression estimator when disturbances are nonnormal. Statistical Papers 44, 233–248 (2003). https://doi.org/10.1007/s00362-003-0148-9
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DOI: https://doi.org/10.1007/s00362-003-0148-9