Experimental designs for regression models

Abstract

This thesis considers the optimal designs for the following five design objectives: (i) Estimation of the mean response; (ii) Estimation of the derivatives of the response function; (iii) Estimation of the difference between mean responses; (iv) Simultaneous estimation of the mean response, the derivatives and the difference; (v) Discrimination between two rival models. For design objectives (i)-(iv) it is assumed that both the postulated and true models are polynomials and the order of the true model is higher than that of the postulated model. It is further assumed that the sum of squares of the parameters excluded from the postulated model is bounded. The design criterion suggested for the first three design objectives is to minimize the average mean squared error (AMSE) maximized over the region of the excluded parameters. Classes of first order minimax AMSE designs are then obtained for design objectives (i)-(iii). Optimal first order designs for design objective (iv) are derived by maximizing the minimum of the efficiencies with respect to the first order minimax AMSE designs for individual design objectives (i)-(iii). Specific first order designs are then chosen via the secondary criteria maximizing the minimum and average of the measure for the lack of fit over the region of the excluded parameters. Such design criteria are equivalent to the maximization of the minimum and average power of the lack of fit test. For the cases where the lack of fit test is significant, second order designs accommodating the optimal first order designs are derived. For design objective (iii) we further obtain the first order designs minimizing AMSE and the second order minimum bias designs for the situations in which the region of the excluded parameters is unknown. For design objective (v) it is assumed that there are two plausible regression models and one is nested within the other. We consider the design criteria maximizing the minimum and average of the measure...