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A short proof of Motoo's combinatorial central limit theorem using Stein's method
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  • Published: June 1988

A short proof of Motoo's combinatorial central limit theorem using Stein's method

  • W. Schneller1 

Probability Theory and Related Fields volume 78, pages 249–252 (1988)Cite this article

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  • 5 Citations

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Summary

A new proof of Motoo's combinatorial central limit theorem (see Motoo 1957) is given using a method of Stein (1972) and a combinatorial method of Bolthausen (1984). This proof is shorter than Motoo's and other wellknown proofs (see e.g. Hájek 1961).

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References

  1. Bolthausen, E.: An estimate of the remainder in a combinatorial central limit theorem. Z. Wahrscheinlichkeitstheor. Verw. Geb. 66, 379–386 (1984)

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  2. Chen, L.H.Y.: Two central limit problems for dependent random variables. Z. Wahrscheinlichkeitstheor. Verw. Geb. 43, 223–243 (1978)

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  3. Hájek, J.: Some extensions of the Wald-Wolfowitz-Noether theorem. Ann. Math. Statist. 32, 506–523 (1961)

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  4. Ho, S.T., Chen, L.H.Y.: An L p bound for the remainder in a combinational central limit theorem. Ann. Probab. 6, 231–249 (1978)

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  7. Stein, Ch.: A bound for the error in the normal approximation to the distribution of a sum of dependent random variables. Proc. Sixth Berkeley Sympos. Math. Statist. Probab. 2, 583–602 (1972)

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Berlin, Straße des 17. Juni 135, D-1000, Berlin 12

    W. Schneller

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  1. W. Schneller
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Schneller, W. A short proof of Motoo's combinatorial central limit theorem using Stein's method. Probab. Th. Rel. Fields 78, 249–252 (1988). https://doi.org/10.1007/BF00322021

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  • Received: 11 June 1987

  • Revised: 13 January 1988

  • Issue Date: June 1988

  • DOI: https://doi.org/10.1007/BF00322021

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Keywords

  • Stochastic Process
  • Stein
  • Probability Theory
  • Limit Theorem
  • Statistical Theory
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