D-optimal design for the heteroscedastic Berman model on an arc

There are various methods for fitting data to circles or ellipses in many different types of applied problems. However, the design of such studies is rarely discussed and for the few that do, model errors are commonly assumed to be homoscedastic and uncorrelated. This paper provides an analytic description of the D-optimal designs for estimating parameters in the bivariate Berman model on an arc when errors are correlated and heteroscedastic. We evaluate D-efficiencies and relative efficiencies of the commonly used equidistant sampling methods and show that such designs can be inefficient.