Optimal unbiased estimation of some population central moments

Mariano Ruiz Espejo, Miguel Delgado Pineda and Saralees Nadarajah ()

METRON, 2013, vol. 71, issue 1, 39-62

Abstract: In this paper, we have treated the problem of estimating some population central moments under distribution-free setting. Uniformly minimum variance unbiased estimators for some population central moments have been derived. Some examples of unbiased estimators of central moments have been given under various sampling designs such as simple random sampling with replacement (srsr) or without replacement (srs), probability proportional to size with replacement (ppsr) and probability graduated variable proportional to size without replacement (pgvps). An optimal unbiased estimator of the third population central moment is proposed and extended to some real situations. Some optimal unbiased estimators of the fourth population central moment are given. Several optimal unbiased estimators of the variance of the “sample quasivariance estimator” are identified. Finally, computer programs in R implementing all of the estimators are given. Copyright Sapienza Università di Roma 2013

Keywords: Distribution free setting; Optimal unbiased estimators; Population central moments; R; Stratified sampling (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:metron:v:71:y:2013:i:1:p:39-62

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DOI: 10.1007/s40300-013-0006-z

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