Algorithms for approximate linear regression design with application to a first order model with heteroscedasticity

The basic structure of algorithms for numerical computation of optimal approximate linear regression designs is briefly summarized. First order methods are contrasted to second order methods. A first order method, also called a vertex direction method, uses a local linear approximation of the optimality criterion at the actual point. A second order method is a Newton or quasi-Newton method, employing a local quadratic approximation. Specific application is given to a multiple first order regression model on a cube with heteroscedasticity caused by random coefficients with known dispersion matrix. For a general (positive definite) dispersion matrix the algorithms work for moderate dimension of the cube. If the dispersion matrix is diagonal, a restriction to invariant designs is legal by equivariance of the model and the algorithms also work for large dimension.