Theoretical evaluation of prediction error in linear regression with a bivariate response variable containing missing data |
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Authors: | Lars Erik Gangsei Trygve Almøy Solve Sæbø |
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Institution: | 1. Animalia - Norwegian Meat and Poultry Research Centre, ?kern, Oslo, Norway;2. Department of Chemistry, Biotechnology, and Food Science, Norwegian University of Life Sciences, ?s, Norwaylars.erik.gangsei@animalia.no;4. Department of Chemistry, Biotechnology, and Food Science, Norwegian University of Life Sciences, ?s, Norway |
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Abstract: | Methods for linear regression with multivariate response variables are well described in statistical literature. In this study we conduct a theoretical evaluation of the expected squared prediction error in bivariate linear regression where one of the response variables contains missing data. We make the assumption of known covariance structure for the error terms. On this basis, we evaluate three well-known estimators: standard ordinary least squares, generalized least squares, and a James–Stein inspired estimator. Theoretical risk functions are worked out for all three estimators to evaluate under which circumstances it is advantageous to take the error covariance structure into account. |
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Keywords: | Bivariate linear regression James–Stein estimator missing data prediction error risk function |
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