Robust bayes and minimax-bayes estimation design in linear regression¹

¹Paper presented to the poster session of the Fourth International Summer School on Problems of Model Choice and Parameter Estimation in Linear Regression, Mühlhausen (G.D.R.), May 1979

Abstract

We consider the problem of the choice of an estimator and an experimental design for estimating the response surface in a linear regression model according to Bayes-and minimax-Bayes-optimality. The well-known Bayes estimator w.r.t. normally i.i.d. observations, conjugate prior distribution and quadratic loss is shown to have a satisfying robustness with regard to the optimality criteria, if we change to larger classes of prior and error distributions (e.g. all distributions with fixed first and second moments) and more general loss functions (e.g. monotone and convex functions). Moreover, for this Bayes estimator we can point out a remarkable robustness of'designing against the loss function; e.g. minimax designs under quadratic loss are also minimax under any convex loss function.

Keywords:

• Linear regression model
• Bayes estimation
• Bayes design
• Minimax-Bayes estimation and design
• robust estimation
• robust design
• G- and I-optimal design

¹Paper presented to the poster session of the Fourth International Summer School on Problems of Model Choice and Parameter Estimation in Linear Regression, Mühlhausen (G.D.R.), May 1979

¹Paper presented to the poster session of the Fourth International Summer School on Problems of Model Choice and Parameter Estimation in Linear Regression, Mühlhausen (G.D.R.), May 1979

Notes

¹Paper presented to the poster session of the Fourth International Summer School on Problems of Model Choice and Parameter Estimation in Linear Regression, Mühlhausen (G.D.R.), May 1979