Minimax Design for Approximate Straight Line Regression

Abstract

This dissertation first reviews the construction of an optimal design for a straight linear regression model with uncorrelated errors when the experimenter seeks protection against the biases which will accrue if her straight line model is slightly erroneous. The optimal design is derived from the minimax method, and is robust against bias caused by a small departure from the fitted model. The study then points out a gap within the part of the minimax method related to minimizing the maximized loss function based on A- and E-optimality criteria: it is not applicable to finding an optimal design for these criteria when the emphasis is much more on the errors from bias than on those from variation. Finally, an alternative technique is applied in order to achieve an A- and E-optimal design whether the experimenter places more emphasis on the errors from bias or on the errors from variance.