### Abstract

We consider f-disparities D_{f}(p̂_{n}, p_{n}) between discrete distributions p_{n} = (p_{n1},..., p_{nkn}) and their estimates p̂_{n} = (p̂_{n1},..., p̂_{nkn}) based on relative frequencies in an i.i.d. sample of size n, where f : (0, ∞) → ℝ is twice continuously differentiable in a neighborhood of 1 with f″(1) ≠ 0. We derive asymptotic distributions of the disparity statistics n D_{f}(p̂_{n}, p_{n}) under certain assumptions about p_{n} and the second derivatives f″ in a neighborhood of 1. These assumptions are weaker than those known from the literature.

Original language | English |
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Pages (from-to) | 57-67 |

Number of pages | 11 |

Journal | Statistics and Probability Letters |

Volume | 56 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2002 |

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### Keywords

- Asymptotic distributions
- Disparity statistics
- Goodness-of-fit statistics
- Goodness-of-fit tests

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Statistics and Probability

### Cite this

**Asymptotic distributions for goodness-of-fit statistics in a sequence of multinomial models.** / Györfi, L.; Vajda, I.

Research output: Contribution to journal › Article

*Statistics and Probability Letters*, vol. 56, no. 1, pp. 57-67. https://doi.org/10.1016/S0167-7152(01)00172-9

}

TY - JOUR

T1 - Asymptotic distributions for goodness-of-fit statistics in a sequence of multinomial models

AU - Györfi, L.

AU - Vajda, I.

PY - 2002/1/1

Y1 - 2002/1/1

N2 - We consider f-disparities Df(p̂n, pn) between discrete distributions pn = (pn1,..., pnkn) and their estimates p̂n = (p̂n1,..., p̂nkn) based on relative frequencies in an i.i.d. sample of size n, where f : (0, ∞) → ℝ is twice continuously differentiable in a neighborhood of 1 with f″(1) ≠ 0. We derive asymptotic distributions of the disparity statistics n Df(p̂n, pn) under certain assumptions about pn and the second derivatives f″ in a neighborhood of 1. These assumptions are weaker than those known from the literature.

AB - We consider f-disparities Df(p̂n, pn) between discrete distributions pn = (pn1,..., pnkn) and their estimates p̂n = (p̂n1,..., p̂nkn) based on relative frequencies in an i.i.d. sample of size n, where f : (0, ∞) → ℝ is twice continuously differentiable in a neighborhood of 1 with f″(1) ≠ 0. We derive asymptotic distributions of the disparity statistics n Df(p̂n, pn) under certain assumptions about pn and the second derivatives f″ in a neighborhood of 1. These assumptions are weaker than those known from the literature.

KW - Asymptotic distributions

KW - Disparity statistics

KW - Goodness-of-fit statistics

KW - Goodness-of-fit tests

UR - http://www.scopus.com/inward/record.url?scp=0036165143&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036165143&partnerID=8YFLogxK

U2 - 10.1016/S0167-7152(01)00172-9

DO - 10.1016/S0167-7152(01)00172-9

M3 - Article

AN - SCOPUS:0036165143

VL - 56

SP - 57

EP - 67

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 1

ER -