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One- and two-term edgeworth expansions for a finite population sample mean. Exact results. I

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Abstract

We prove the validity of one- and two-term Edgeworth expansions under optimal conditions (a Cramer-type smoothness condition and the minimal moment conditions) and provide precise bounds for the remainders of expansions. The bounds depend explicitly on the ratiop=N/n, whereN andn denote the sample size and the population size, respectively.

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Authors and Affiliations

  1. Vilnius University, Naugarduko 24, 2600, Vilnius, Lithuania

    M. Bloznelis

  2. Institute of Mathematics and Informatics, Akademijos 4, 2600, Vilnius, Lithuania

    M. Bloznelis

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  1. M. Bloznelis
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Supported by the Alexander von Humboldt Foundation.

Published in Lietuvos Matematikos Rinkinys, Vol. 40, No. 3, pp. 277–294, July–September, 2000.

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Bloznelis, M. One- and two-term edgeworth expansions for a finite population sample mean. Exact results. I. Lith Math J 40, 213–227 (2000). https://doi.org/10.1007/BF02465130

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  • DOI: https://doi.org/10.1007/BF02465130

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