Optimal design: Regression models for directions

Abstract

Optimal designs are described for three cases. In the first, the dependent variable is a scalar which regresses on a direction, using the trigonometric or spherical harmonic systems. In the next case, the predictors are scalars whilst the regressor is a direction; models for this situation were introduced by Gould (1969). In the third case both the predictors and the regressor are directions, and a vector regression is suggested.