This paper studies the estimation of the characteristic function of a finite
population. Specifically, the weak convergence of the finite population empirical
characteristic process is studied. Under suitable assumptions, it has the same limit
as the empirical characteristic process for independent, identically distributed data
from a random variable, up to a multiplicative constant depending on the sampling
design. Applications of the obtained results for the two-sample problem, testing for
independence and testing for symmetry are given.

EB00000004438K

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• On the estimation of the characteristic function in finite populations with applications