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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Bolthausen, E.: An estimate of the remainder in a combinatorial central limit theorem. Z. Wahrscheinlichkeitstheor. Verw. Geb. 66, 379–386 (1984)
Chen, L.H.Y.: Two central limit problems for dependent random variables. Z. Wahrscheinlichkeitstheor. Verw. Geb. 43, 223–243 (1978)
Hájek, J.: Some extensions of the Wald-Wolfowitz-Noether theorem. Ann. Math. Statist. 32, 506–523 (1961)
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)
Hoeffding, W.: A combinatorial central limit theorem. Ann. Math. Statist. 22, 558–566 (1951)
Motoo, M.: On the Hoeffding's combinatorial central limit theorem. Ann. Inst. Stat. Math. 8, 145–154 (1957)
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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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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DOI: https://doi.org/10.1007/BF00322021