Improved estimation in multiple linear regression models with measurement error and general constraint

Journal of Multivariate Analysis

Volumn 100, Issue 4, 2009, Pages 726-741

  Liang, Hua ^a   Song, Weixing ^b  

^a UNIVERSITY OF ROCHESTER MEDICAL CENTER   (United States)

^b KANSAS STATE UNIVERSITY   (United States)

Author keywords

62F30; 62J05; 62J99; Asymptotic distributional quadratic bias; Asymptotic distributional quadratic risk; Attenuation correction estimator; James Stein type estimator; Positive rule Stein type estimator; Preliminary test estimator; primary; Risk function; secondary

Indexed keywords

EID: 58349122248     PISSN: 0047259X     EISSN: 10957243     Source Type: Journal    
DOI: 10.1016/j.jmva.2008.08.003     Document Type: Article

References (21)

1. Judge G.G., and Bock M.E. The Statistical Implications of Pre-test and Stein-Rule Estimators in Econometrics (1978), North Holland Publication, New York
2. Saleh A.K.Md.E. Theory of Preliminary Test and Stein-Type Estimation with Application (2006), Wiley & Sons, New York
3. Bancroft T.A. On biases in estimation due to the use of preliminary tests of significance. Ann. Math. Statist. 15 (1944) 190-204
4. Saleh A.K.Md.E., and Sen P.K. On shrinkage least-squares estimation in a parallelism problem. Ann. Statist. 6 (1978) 154-168
5. C. Stein, Inadmissibility of the usual estimator for the mean of a multivariate normal distribution, in: Proceedings of the Third Berkeley Symposium on Mathematics and Statistical Probability, vol. 1, 1956, pp. 197-206
6. W. James, C. Stein, Estimation with quadratic loss, in: Proceedings of the Fourth Berkeley Symposium on Mathematics and Statistical Probability, vol. 1, 1961, pp. 361-379
7. Saleh A.K.Md.E., and Sen P.K. Non-parametric estimation of location parameter after a preliminary test regression. Commun. Statist. 15 (1986) 1451-1466
8. Sen P.K., and Saleh A.K.Md.E. On preliminary test and shrinkage M-estimation in linear models. Ann. Statist. 15 (1987) 1580-1592
9. Stanley T.D. Stein rule least squares estimation, a heuristic for fallible data. Econ. Lett. 20 (1986) 147-150
10. Stanley T.D. Improved estimators in some linear errors-in-variables models in finite samples. J. Forecasting 7 (1988) 103-113
11. Shalabh. Improved estimation in measurement error models through Stein rule procedure. J. Mult. Anal. 67 (1998) 35-48
12. Kim H.M., and Saleh A.K.Md.E. Preliminary test estimators of the parameters of simple linear model with measurement error. Metrika 57 (2003) 223-251
13. Kim H.M., and Saleh A.K.Md.E. Improved estimation of regression parameters in measurement error models. J. Mult. Anal. 95 (2005) 273-300
14. Gleser L.J. The importance of assessing measurement reliability in multivariate regression. J. Am. Statist. Assoc. 87 (1992) 696-707
15. Goel P.K., and DeGroot M.H. Only normal distributions have linear posterior expectations in linear regression. J. Am. Statist. Assoc. 75 (1980) 895-900
16. Rao C.R. Characterization of prior distributions and solutions to a compound decision problem. Ann. Statist. 4 (1976) 823-835
17. Fuller W.A. Measurement Error Models (1987), Wiley & Sons, New York
18. Carroll R.J., Ruppert D., Stefanski L.A., and Crainiceanu C.M. Measurement Error in Nonlinear Models. 2nd ed. (2006), Chapman and Hall, New York
19. Schneeweiss. Consistent estimation of a regression with errors in the variables. Metrika 23 (1976) 101-115
20. Rosner B., Spiegelman D., and Willett W.C. Correction of logistic regression relative risk estimates and confidence intervals for measurement error: The case of multiple covariates measured with error. Am. J. Epidemiol. 132 (1990) 734-735
21. Liang H., Härdle W., and Carroll R.J. Estimation in a semiparametric partially linear errors-in-variables model. Ann. Statist. 27 (1999) 1519-1535