Statistica Sinica **11**(2001), 261-272

Julie Zhou

Abstract:In this paper, infinitesimal and minimax approaches are used to construct robust regression designs for linear models with correlated errors. We consider IMSE (Integrated Mean Squared Error) as the loss function. Using an infinitesimal approach, we minimize IMSE at the ideal model subject to two robust constraints to derive M-robust designs. We also minimize the maximum of the IMSE to obtain minimax designs. In particular, M-robust and minimax designs are constructed for an approximately linear model with MA(1) errors. These designs are robust against small departures from the assumed regression response and small departures from the assumption of uncorrelated errors. It is interesting that M-robust and minimax designs have the same form of density function, while M-robust designs require less restrictive ordering of design points. Implementation is discussed and examples are given.

Key words and phrases:Approximately linear regression response, infinitesimal approach, M-robust design, minimax design, moving average errors, robust regression design.