### Abstract

It is shown that under appropriate conditions the sth cumulant of a von Mises statistic or a U (or V) statistic is O(n
^{-s+1}
), s ≥ 2, as the sample size n goes to infinity. A possible route toward the derivation of an asymptotic expansion of the characteristic function is indicated.

Original language | English (US) |
---|---|

Title of host publication | Probability Theory and Extreme Value Theory |

Publisher | De Gruyter Mouton |

Pages | 54-62 |

Number of pages | 9 |

Volume | 2 |

ISBN (Electronic) | 9783110917826 |

ISBN (Print) | 9789067643856 |

State | Published - Jul 11 2011 |

Externally published | Yes |

### Keywords

- Edgeworth expansion
- U-statistics
- V-Statistics

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Bhattacharya, R. N., & Puri, M. L. (2011). On the order of magnitude of cumulants of von Mises functionals and related statistics. In

*Probability Theory and Extreme Value Theory*(Vol. 2, pp. 54-62). De Gruyter Mouton.