On the estimation of the characteristic function in finite populations with applications
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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.
KeywordsFinite population Design-based inference High entropy designs Characteristic function Test for the two-sample problem Test for independence Test for symmetry
Mathematics Subject Classification62D05 62G10 62G09
The authors thank the anonymous referees and the Associate Editor for their valuable time and careful comments, which improved the quality of this paper. M. D. Jiménez-Gamero acknowledges financial support from Grant MTM2014-55966-P of the Spanish Ministry of Economy and Competitiveness.