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

L. Györfi, I. Vajda

Research output: Article

13 Citations (Scopus)

### Abstract

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.

Original language English 57-67 11 Statistics and Probability Letters 56 1 https://doi.org/10.1016/S0167-7152(01)00172-9 Published - jan. 1 2002

### Fingerprint

Multinomial Model
Goodness of fit
Asymptotic distribution
Statistics
Discrete Distributions
Continuously differentiable
Second derivative
Estimate
Derivatives
Discrete distributions

### ASJC Scopus subject areas

• Statistics, Probability and Uncertainty
• Statistics and Probability

### Cite this

In: Statistics and Probability Letters, Vol. 56, No. 1, 01.01.2002, p. 57-67.

Research output: Article

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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.

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