A-Optimum Exact Designs for Quadratic Regression

Shrinkage simplex-centroid designs for a quadratic mixture model

A simplex-centroid design for q mixture components comprises of all possible subsets of the q components, present in equal proportions. The design does not contain full mixture blends except the overall centroid. In real-life situations, all mixture blends comprise of at least a minimum proportion of each component. Here, we introduce simplex-centroid designs which contain complete blend...

Optimal experimental designs for inverse quadratic regression models

In this paper optimal experimental designs for inverse quadratic regression models are determined. We consider two different parameterizations of the model and investigate local optimal designs with respect to the c-, Dand Ecriteria, which reflect various aspects of the precision of the maximum likelihood estimator for the parameters in inverse quadratic regression models. In particular it is d...

Computing efficient exact designs of experiments using integer quadratic programming

We propose a method of computing exact experimental designs by integer quadratic programming. The key idea is a suitable quadratic approximation of the criterion of D-optimality in the neighbourhood of the approximate D-optimal information matrix, which we call the criterion of Q-optimality. We demonstrate on several examples that the D-efficiency of the exact Q-optimal designs is usually very ...

Integral approximations for computing optimum designs in random effects logistic regression models

In the context of nonlinear models, the analytical expression of the Fisher information matrix is essential to compute optimum designs. The Fisher information matrix of the random effects logistic regression model is proved to be equivalent to the information matrix of the linearized model, which depends on some integrals. Some algebraic approximations for these integrals are proposed, which ar...

Exact solutions for the flow of a generalized second grade due to a Longitudinal quadratic time-dependent shear stress