Unbiased Estimates for Products of Moments and Cumulants for Finite Populations

Christopher S. Withers and Saralees Nadarajah ()
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Christopher S. Withers: Callaghan Innovation, Lower Hutt 5011, New Zealand
Saralees Nadarajah: Department of Mathematics, University of Manchester, Manchester M13 9PL, UK

Mathematics, 2023, vol. 11, issue 17, 1-36

Abstract: Let F N be the distribution function of a finite real population of size N . Let F n be the empirical distribution function of a sample of size n drawn from the population without replacement. Let T F N be any product of the moments or cumulants of F N , let T F n denote the sample version, and let T n , N F N denote the expected value of T F n with respect to F N . We prove the following remarkable inversion principle that the expected value of T N , n F n is equal to T F N . We also obtain an explicit expression for T n , N F N for all T F N of orders up to six.

Keywords: cumulants; finite population; moments; unbiased estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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