Minimaxschätzungen im linearen regressionsmodell
- 1 January 1972
- journal article
- research article
- Published by Taylor & Francis in Mathematische Operationsforschung und Statistik
- Vol. 3 (6) , 475-482
- https://doi.org/10.1080/02331887208801102
Abstract
If the errors of a linear model are normally distributed and if quadratic loss is used, it is known, that the Gauss-Markov-estimator is the best unbiased estimator of an estimable function η. Under certain conditions this is also true for convex loss. It we know only, that the error distribution lies in a certain class of distributions, and the normal distribution is in this class too, then, it is shown, that becomes minimax relative to this class.Keywords
This publication has 3 references indexed in Scilit:
- Monotonieeigenschaften stochastischer ModelleZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1972
- Schätzungen im linearen Regressionsmodell bei konvexem VerlustBiometrische Zeitschrift, 1971
- On Best Linear Estimation and General Gauss-Markov Theorem in Linear Models with Arbitrary Nonnegative Covariance StructureSIAM Journal on Applied Mathematics, 1969