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Original Articles

Best Quadratic Unbiased Prediction in a General Linear Model with Stochastic Regression Coefficients

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Pages 1418-1433 | Received 12 May 2008, Accepted 05 Jan 2010, Published online: 19 Feb 2011

References

  • Baksalary , J. K. , Mathew , T. ( 1986 ). Linear sufficiency and completeness in an incorrectly specified general Gauss–Markov model . Sankhy A 48 : 169 – 180 .
  • Berstein , D. S. ( 2009 ). Matrix Mathematics: Theory, Facts and Formulas. , 2nd ed. Princeton , NJ : Pinceton Univeristy Press .
  • Bolfarine , H. , Zacks , S. , Elian , S. N. , Rodrigues , J. ( 1994 ). Optimal prediction of the finite population regression coefficient . Sankhy Ser. B 56 : 1 – 10 .
  • Chang , I. , Swamy , P. A. V. B. , Hallahan , C. , Tavlas , G. S. ( 2000 ). A computational approach to finding causal economic laws . Computat. Econ. 16 : 105 – 136 .
  • Drygas , H. ( 1985 ). Linear sufficiency and some applications in multilinear estimation . J. Multivariate Anal. 16 : 71 – 84 .
  • Fang , K. , Zhang , Y. ( 1993 ). Generalized Multivariate Analysis . Beijing : Science Press (in Chinese) .
  • Gnot , S. , Grzadziel , M. ( 2002 ). Nonnegative minimum biased quadratic estimation in mixed linear models . J. Multivariate Anal. 80 : 217 – 233 .
  • Gnot , S. , Trenkler , G. , Zmyślony , R. ( 1995 ). Nonnegative minimum biased quadratic estimation in the linear regression models . J. Multivariate Anal. 54 : 113 – 125 .
  • Groß , J. ( 1998 ). A note on the concepts of linear and quadratic sufficiency . J. Statist. Plann. Infer. 70 : 69 – 76 .
  • Heiligers , B. , Markiewicz , A. ( 1996 ). Linear sufficiency and admissibility in restricted linear models . Statist. Probab. Lett. 30 : 105 – 111 .
  • Ibarrola , P. , Pérez-Palomares , A. ( 2003 ). Linear sufficiency and linear admissibility in a continuous time Gauss–Markov model . J. Multivariate Anal. 87 : 315 – 327 .
  • Isotalo , J. , Puntanen , S. ( 2006 ). Linear prediction sufficiency for new observations in the general Gauss–Markov model . Commun. Statist. A 35 : 1011 – 1023 .
  • Kashyap , A. K. , Swamy , P. A. V. B. , Mehta , J. S. , Porter , R. D. ( 1988 ). Further results on estimating linear regression models with partial prior information . Econ. Model. 1 : 49 – 57 .
  • Khuri , A. , Mathew , T. , Sinha , B. ( 1998 ). Statistical Tests for Mixed Linear Models . New York : Wiley .
  • Lehmann , E. L. , Casella , G. ( 1998 ). Theory of Point Estimation. , 2nd ed. New York : Springer .
  • Liu , X. Q. , Rong , J. Y. ( 2007 ). Nonnegative quadratic estimation and quadratic sufficiency in general linear models . J. Multivariate Anal. 98 : 1180 – 1194 .
  • Liu , X. Q. , Rong , J. Y. , Liu , X. Y. ( 2008a ). Best linear unbiased prediction for linear combinations in general mixed linear models . J. Multivariate Anal. 99 : 1503 – 1517 .
  • Liu , X. Q. , Rong , J. Y. , Zhuang , Y. M. ( 2008b ). On quadratic prediction problems in finite populations . J. Statist. Plann. Infer. 138 : 3257 – 3268 .
  • Müeller , J. ( 1987 ). Sufficiency and completeness in the linear model . J. Multivariate Anal. 21 : 312 – 323 .
  • Rao , C. R. , Toutenburg , H. (1995). Linear Models: Least Squares and Alternatives . New York : Springer.
  • Schott , J. R. ( 2003 ). Kronecker product permutation matrices and their application to moment matrices of the normal distribution . J. Multivariate Anal. 87 : 177 – 190 .
  • Ste¸pniak , C. ( 1998 ). On admissibilty in estimating the mean squared error of a linear estimator . Probab. Mathemat. Statist. 18 : 33 – 38 .
  • Swamy , P. A. V. B. , Mehta , J. S. ( 1975 ). Bayesian and non-bayesian analysis of switching regressions and of random coefficient regression models . J. Amer. Statist. Assoc. 70 : 593 – 602 .
  • Swamy , P. A. V. B. , Tinsley , P. A. ( 1980 ). Linear prediction and estimation methods for regression models with stationary stochastic coefficients . J. Econometrics 12 : 103 – 142 .
  • Swamy , P. A. V. B. , Yaghi , W. , Mehta , J. S. , Chang , I. ( 2007 ). Empirical best linear unbiased prediction in misspecified and improved panel data models with an application to gasoline demand . Computat. Statist. Data Anal. 51 : 3381 – 3392 .
  • Wang , S. ( 1987 ). Theory of Linear Models and Its Applications . China : Anhui Education Press. (in Chinese) .

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