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Improved estimation in regression with varying penalty. (English) Zbl 1426.62200

Summary: This article considers the estimation of the intercept parameter of a simple linear regression model under asymmetric linex loss. The least-squares estimator (LSE) and the preliminary test estimator (PTE) are defined. The risk functions of the estimators are derived. The moment-generating function (MGF) and the first two moments of the PTE are shown. The risk of the PTE is compared with that of the LSE. The analyses show that if the nonsample prior information about the value of the parameter is not too far from its true value, the PTE dominates the traditional LSE.

MSC:

62J05 Linear regression; mixed models
62F10 Point estimation
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[1] Bhoj, D. and M. Ahsanullah. 1993. Estimation of a conditional mean in a regression model. Biometrics J., 37, 791-799. · doi:10.1002/bimj.4710350705
[2] Bhoj, D. and M. Ahsanullah. 1994. Estimation of a conditional mean in a linear regression model after a preliminary test on regression coefficient. Biometrics. J., 36, 153-163. · Zbl 0850.62494 · doi:10.1002/bimj.4710360206
[3] Bancroft, T. A. 1944. On biases in estimation due to the use of the preliminary test of significance. Ann. Math. Stat., 15, 190-204. · Zbl 0063.00180 · doi:10.1214/aoms/1177731284
[4] Bhattacharaya, D., F. J. Samaniego, and E. M. Vestrup. 2002. On the comperative performance of bayesian and classical point estimators under asymmetric loss. Sankhya B, 64(3), 239-266. · Zbl 1192.62059
[5] Hoque, Z. 2004. Improved estimation of linear models under different loss functions. Unpublished PhD thesis, University of Southern Queensland, Australia.
[6] Khan, S., Z. Hoque, and A. K. M. E. Saleh. 2002. Estimation of the slope parameter for linear regression model with uncertain prior information. J. Stat. Res., 36(1), 55-73.
[7] Khan, S., Z. Hoque, and A. K. M. E. Saleh. 2005. Estimation of the intercept parameter for linear regression mopdel with uncertain prior information. Stat. Papers., 46(3), 379-398. · Zbl 1082.62019 · doi:10.1007/BF02762840
[8] Pandey, B. N., and O. Rai. 1992. Bayesian estimation of mean and square of mean of normal distribution using linex loss function. Commun. Stat. Theory Methods, 21(12), 3369-3391. · Zbl 0777.62033 · doi:10.1080/03610929208830985
[9] Parsian, A., and N. S. Farispour, 1993. On the admissibility and inadmissibility of estimators of scale parameters using an asymmetric loss function. Commun. Stat. Theory Methods, 22(10), 2877-2901. · Zbl 0785.62007 · doi:10.1080/03610929308831191
[10] Parsian, A., N. S. Farispour, and N. Nematollahi. 1993. On the minimaxity of pitman type estimator under a linex loss function. Commun. Stat. Theory Methods, 22(1), 97-113. · Zbl 0777.62011 · doi:10.1080/03610929308831008
[11] Rojo, J. 1987. On the admissibility of cX¯ + d with respect to the linex loss function. Commun. Stat.Theory Methods, 16(12), 3745-3748. · Zbl 0651.62007 · doi:10.1080/03610928708829603
[12] Saleh, A. K. M. E., 2006. Theory of preliminary test and stein-type estimation with applications. New York, NY, John Wiley. · Zbl 1094.62024 · doi:10.1002/0471773751
[13] Saleh, A. K. M. E. and C. P. Han 1990. Shrinkage estimation in regression analysis. Estadistica, 42, 40-63.
[14] Saleh, A. K M. E.; Sen, P. K., Shrinkage least squares estimation in a general multivari-ate linear model, 275-297 (1985)
[15] Saleh, A. K. M. E. and P. K. Sen. 1986. On shrinkage R-estimation in a multiple regression model. Commun. Stat. Theory Methods, 15(7), 2229-2244. · Zbl 0609.62110 · doi:10.1080/03610928608829245
[16] Varian, H. R.; Feinberg, S. E (ed.); Zellner, A. (ed.), A Bayesian approach to real estate assessment, 195-208 (1975), Amsterdam
[17] Zellner, A. 1986. Bayesian estimation and prediction using asymmetric loss functions. J. Am. Stat. Assoc., 81(394), 446-451. · Zbl 0603.62037 · doi:10.1080/01621459.1986.10478289
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