$D$-optimal experimental designs for linear multiple regression under heteroscedastic observations

The problem of construction of «continuous» (number of observations is not fixed) and «exact» (number of observations is fixed) $D$-optimal experimental designs for linear multiple regression in the case when variance of errors of observations depends on regressor value is studied in this paper. Families of functions that determine heteroscedastic observations are found for which it is possible to construct «continuous» and «exact» $D$-optimal experimental designs. «Continuous» $D$-optimal experimental designs under four different types of heteroscedasticity are constructed for linear multiple regression with three regressors.