Exact <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$D$$</EquationSource> </InlineEquation>-optimal designs for first-order trigonometric regression models on a partial circle

Recently, various approximate design problems for low-degree trigonometric regression models on a partial circle have been solved. In this paper we consider approximate and exact optimal design problems for first-order trigonometric regression models without intercept on a partial circle. We investigate the intricate geometry of the non-convex exact trigonometric moment set and provide characterizations of its boundary. Building on these results we obtain a solution of the exact <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$D$$</EquationSource> </InlineEquation>-optimal design problem. It is shown that the structure of the optimal designs depends on both the length of the design interval and the number of observations. Copyright Springer-Verlag Berlin Heidelberg 2013