### 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 |

### Fingerprint

### Keywords

- Edgeworth expansion
- U-statistics
- V-Statistics

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

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

**On the order of magnitude of cumulants of von Mises functionals and related statistics.** / Bhattacharya, Rabindra N; Puri, M. L.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

}

TY - CHAP

T1 - On the order of magnitude of cumulants of von Mises functionals and related statistics

AU - Bhattacharya, Rabindra N

AU - Puri, M. L.

PY - 2011/7/11

Y1 - 2011/7/11

N2 - 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.

AB - 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.

KW - Edgeworth expansion

KW - U-statistics

KW - V-Statistics

UR - http://www.scopus.com/inward/record.url?scp=85064884224&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85064884224&partnerID=8YFLogxK

M3 - Chapter

AN - SCOPUS:85064884224

SN - 9789067643856

VL - 2

SP - 54

EP - 62

BT - Probability Theory and Extreme Value Theory

PB - De Gruyter Mouton

ER -