D-optimal designs for full and reduced Fourier regression models (Q1685220)

Consider trigonometric regression models having basis functions of the type \(1\), \(\sin(jt)\), \(\cos(jt)\), \(j=1,\dots,m\), unknown parameters \(\beta_0,\beta_{2j-1}\), \(\beta_{2j}\), \(j=1,\dots,m\), resp., sets of design support points \(I=\{t_1,\dots,t_n\}\), and uncorrelated, zero-mean random errors \(\epsilon_t\), \(t \in I\), with variance \(\sigma^2\). Considering designs, represented by discrete probability measures \(\xi\) on \(I\), D-optimal designs -- minimizing the determinant of the covariance matrix of the parameter estimator -- are given for different types of trigonometric regression models. Especially, D-optimal designs for estimating pairs of coefficients related to sine and cosine terms are taken into account. Comparisons of the models under considerations are presented.