Admissible prediction in superpopulation models with random regression coefficients under matrix loss function

Admissible prediction problems in finite populations with arbitrary rank under matrix loss function are investigated. For the general random effects linear model, we obtained the necessary and sufficient conditions for a linear predictor of the linearly predictable variable to be admissible in the two classes of homogeneous linear predictors and all linear predictors and the class that contains all predictors, respectively. Moreover, we prove that the best linear unbiased predictors (BLUPs) of the population total and the finite population regression coefficient are admissible under different assumptions of superpopulation models respectively.

[1]  R. Royall,et al.  Robust Estimation in Finite Populations I , 1973 .

[2]  Admissible estimation of linear functions of characteristic values of a finite population , 1997 .

[3]  D. Basu,et al.  Statistical Information and Likelihood , 2011 .

[4]  C. Radhakrishna Rao,et al.  Estimation of parameters in a linear model , 1976 .

[5]  Heleno Bolfarine,et al.  Bayes and minimax prediction in finite populations , 1991 .

[6]  R. Royall.  On finite population sampling theory under certain linear regression models , 1970 .

[7]  L. Lamotte.  On Admissibility and Completeness of Linear Unbiased Estimators in a General Linear Model , 1977 .

[8]  S. Zontek.  On characterization of linear admissible estimators: An extension of a result due to C. R. Rao , 1987 .

[9]  Xu-Qing Liu,et al.  Quadratic prediction problems in multivariate linear models , 2009, J. Multivar. Anal..

[10]  Roman Józef Zmyślony,et al.  On estimation of parameters in linear models , 1976 .

[11]  S. Yu,et al.  ADMISSIBILITY OF LINEAR PREDICTION UNDER QUADRATIC LOSS , 2004 .

[12]  Josemar Rodrigues,et al.  Robust Linear Prediction in Finite Populations , 1983 .

[13]  Heleno Bolfarine,et al.  Prediction Theory for Finite Populations , 1992 .

[14]  Xu Liwen.  The Minimax Predictor in the Finite Populations with Arbitrary Rank in Normal Distribution , 2006 .

[15]  Yuan Shenghua.  THE LINEAR MINIMAX PREDICTOR IN FINITE POPULATIONS WITH ARBITRARY RANK UNDER QUADRATIC LOSS FUNCTION , 2004 .

[16]  On predicting the population total under regression models with measurement errors , 1996 .

[17]  Jian-Ying Rong,et al.  Quadratic prediction problems in finite populations , 2007 .

[18]  Liwen Xu,et al.  Admissible Linear Predictors in the Superpopulation Model with Respect to Inequality Constraints , 2009 .

[19]  C. Stepniak.  Admissible linear estimators in mixed linear models , 1989 .

[20]  Admissible Estimation for Finite Population When the Parameter Space is Restricted , 2002 .

[21]  Arthur Cohen,et al.  All Admissible Linear Estimates of the Mean Vector , 1966 .

[22]  T. Postelnicu,et al.  Foundations of inference in survey sampling , 1977 .

[23]  Yuan Shenghua.  Admissibility of linear predictor in multivariate linear model with arbitrary rank , 2004 .

[24]  David Birkes,et al.  Invariant Quadratic Unbiased Estimation for Two Variance Components , 1976 .

[25]  L. Lamotte.  Admissibility in Linear Estimation , 1982 .