Abstract
Arnold and Stahlecker (Stat Pap 44:107–115, 2003) considered the prediction of future values of the dependent variable in the linear regression model with a relative squared error and deterministic disturbances. They found an explicit form for a minimax linear affine solution d* of that problem. In the paper we generalize this result proving that the decision rule d* is also minimax when the class \({\mathcal{D}}\) of possible predictors of the dependent variable is unrestricted. Then we show that d* remains minimax in \({\mathcal{D}}\) when the disturbances are random with the mean vector zero and the known positive definite covariance matrix.
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Wilczyński, M. Minimax prediction in the linear model with a relative squared error. Stat Papers 53, 151–164 (2012). https://doi.org/10.1007/s00362-010-0325-6
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DOI: https://doi.org/10.1007/s00362-010-0325-6