Sufficient and admissible estimators in general multivariate linear model |
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| Institution: | 1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;2. Department of Mathematics, College of Sciences, South China Agricultural University, Guangzhou 510642, PR China;1. Department of Statistics, Grossman Center for the Statistics of Mind, Zuckerman Mind Brain Behavior Institute, Center for Theoretical Neuroscience, Columbia University, United States;2. Department of Neuroscience, Grossman Center for the Statistics of Mind, Zuckerman Mind Brain Behavior Institute, Center for Theoretical Neuroscience, Columbia University, United States;1. Miembro de la Carrera del Investigador Científico, Consejo de Investigaciones de la Universidad Nacional de Rosario (CIUNR), Rosario, Santa Fe, Argentina;2. Centro de Medicina Tropical y Enfermedades Infecciosas Emergentes, Facultad de Ciencias Médicas, Universidad Nacional de Rosario, Rosario, Santa Fe, Argentina;1. China Economics and Management Academy, Central University of Finance and Economics, Beijing, China;2. School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China;1. Gerencia de Gestión Integrada de Pontevedra, Servicio Gallego de Salud, Caldas de Reis, Pontevedra, Spain;2. Central de Coordinación de Urgencias 061, Fundación Pública Urgencias Sanitarias de Galicia-061, Santiago de Compostela, La Coruña, Spain;3. Predicción Operativa, MeteoGalicia, Santiago de Compostela, La Coruña, Spain;4. Laboratorio de Bioingeniería y Cronobiología, Universidad de Vigo, Vigo, Pontevedra, Spain;5. Servicio de Docencia e Investigación, Fundación Pública Urgencias Sanitarias de Galicia-061, Santiago de Compostela, La Coruña, Spain |
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| Abstract: | The notion of linear sufficiency in general Gauss–Markov model is extended to a general multivariate linear model for any specific set of estimable functions. A general formula of the difference between the dispersion matrix of the BLUE in the original model and that in the transformed model is provided, which brings some further contributions to the theory of linear sufficiency. Moreover, a general formula of the change of BLUE due to transformation is obtained. The analysis here leads to some results, some of which are known in the literature. Besides linear sufficiency, the admissibility of a linear statistic is also extended to the multivariate case. |
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