Some optimal sampling designs in the presence of polynomial trends
We consider the problem of optimal estimation of a finite population mean in the presence of polynomial trends and suggest different methods of construction of associated optimal sampling designs for various specific combinations of values of the population size N and the sample size n. Particularly for the case of quadratic trend, we give a complete listing of all such existent designs for N< 18 and also give necessary and sufficient conditions for the existence of such optimal sampling designs when N = nk, k = 2,3,4,6.