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A central limit theorem for certain nonlinear statistics in repeated sampling of a finite population

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  • Hawkins, D. L.
  • Han, Chien-Pai

Abstract

We prove a central limit theorem for the asymptotic joint distribution of non-linear statistics of the form [summation operator]l = 1N XNltItlIt+1,l, 1 [less-than-or-equals, slant] t [less-than-or-equals, slant] r - 1, and linear statistics of the form [summation operator]l = 1N XNltItl, 1 [less-than-or-equals, slant] t [less-than-or-equals, slant] r, based on independent repeated samples of a finite population of size N with sample indicators Itl,l = 1, ..., N, for the tth sample.

Suggested Citation

  • Hawkins, D. L. & Han, Chien-Pai, 1998. "A central limit theorem for certain nonlinear statistics in repeated sampling of a finite population," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 25-34, July.
    • Handle: RePEc:eee:stapro:v:39:y:1998:i:1:p:25-34
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    References listed on IDEAS

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    1. White, Donald B., 1988. "An application of a multivariate central limit theorem to sampling without replacement," Journal of Multivariate Analysis, Elsevier, vol. 24(1), pages 123-128, January.
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    Cited by:

    1. D. L. Hawkins & Chien-Pai Han, 2000. "Estimating Transition Probabilities from Aggregate Samples Plus Partial Transition Data," Biometrics, The International Biometric Society, vol. 56(3), pages 848-854, September.

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