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Lower estimation of the remainder term in the CLT for a sum of the functions of k-spacings

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  • Mirakhmedov, Sherzod A.

Abstract

The main result is lower estimation of the remainder term in the central limit theorem for a sum of the functions of disjoint uniform k-spacings. From this result, the Lindeberg's type condition of asymptotical normality and Berry-Esséen's type bound is derived. Note that here k=k(n) may tend to infinity if sample size n-->[infinity].

Suggested Citation

  • Mirakhmedov, Sherzod A., 2005. "Lower estimation of the remainder term in the CLT for a sum of the functions of k-spacings," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 411-424, July.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:4:p:411-424
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    Citations

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    Cited by:

    1. M. Ekström & S. M. Mirakhmedov & S. Rao Jammalamadaka, 2020. "A class of asymptotically efficient estimators based on sample spacings," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 617-636, September.
    2. Ibrahim Bin Mohamed & Sherzod M. Mirakhmedov, 2016. "Approximation by Normal Distribution for a Sample Sum in Sampling Without Replacement from a Finite Population," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 188-220, August.
    3. Sherzod Mirakhmedov & Syed Tirmizi & Muhammad Naeem, 2011. "A Cramér-type large deviation theorem for sums of functions of higher order non-overlapping spacings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(1), pages 33-54, July.
    4. Rahul Singh & Neeraj Misra, 2023. "Some parametric tests based on sample spacings," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 211-231, March.
    5. S. M. Mirakhmedov & S. Rao Jammalamadaka & Ibrahim B. Mohamed, 2014. "On Edgeworth Expansions in Generalized Urn Models," Journal of Theoretical Probability, Springer, vol. 27(3), pages 725-753, September.

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