Summary
In estimating the mean μ y of one variable in a bivariate normal distribution, the experimenter can use the other variable,x, as an auxiliary variable to increase precision. In particular, if μ x is known, he can use the regression estimator. When μ x is unknown, a preliminary test can be performed and the estimator will be made to depend on the result of the preliminary test. The bias and mean square error of the preliminary test estimator are obtained and the relative efficiency is are discussed.
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References
Bancroft, T. A. (1944). On biases in estimation due to the use of preliminary tests of significance,Ann. Math. Statist.,15, 190–204.
Bennett, B. M. (1952). Estimation of means on the basis of preliminary tests of significance,Ann. Inst. Statist. Math.,4, 31–43.
Dempster, A. P. (1969).Elements of Continuous Multivariate Analysis, Addison-Wesley, Reading, Massachusetts.
Han, C. P. and Bancroft, T. A. (1968). On pooling means when variance is unknown,Jour. Amer. Statist. Assoc.,63, 1333–1342.
Kale, B. K. and Bancroft, T. A. (1967). Inference for some incompletely specified models involving normal approximations to discrete data,Biometrics,23, 335–348.
Kitagawa, Tosio (1963). Estimation after preliminary tests of significance,Univ. Cal. Pub. in Statist.,3, 147–186.
Mosteller, Frederick (1948). On pooling data,Jour. Amer. Statist. Assoc.,43, 231–242.
Rao, C. R. (1965).Linear Statistical Inference and Its Application, John Wiley, New York.
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Han, CP. Regression estimation for bivariate normal distributions. Ann Inst Stat Math 25, 335–344 (1973). https://doi.org/10.1007/BF02479379
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DOI: https://doi.org/10.1007/BF02479379