Abstract
We study the rate of weak convergence of the distributions of the statistics {tλ(Y), λ ∈ ℝ} from the power divergence family of statistics to the χ2 distribution. The statistics are constructed from n observations of a random variable with three possible values. We show that, where G2(c) is the χ2 distribution function of a random variable with two degrees of freedom. In the proof we use Huxley's theorem of 1993 on approximating the number of integer points in a plane convex set with smooth boundary by the area of the set.
| Original language | English |
|---|---|
| Pages (from-to) | 571-584 |
| Number of pages | 14 |
| Journal | Siberian Mathematical Journal |
| Volume | 52 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Jul 2011 |
| Externally published | Yes |
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Keywords
- accuracy of χ approximation
- Huxley theorem
- integer points
- power divergence family of statistics
ASJC Scopus subject areas
- Mathematics(all)
Cite this
On approximating some statistics of goodness-of-fit tests in the case of three-dimensional discrete data. / Asylbekov, Zh A.; Zubov, V. N.; Ulyanov, V. V.
In: Siberian Mathematical Journal, Vol. 52, No. 4, 07.2011, p. 571-584.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - On approximating some statistics of goodness-of-fit tests in the case of three-dimensional discrete data
AU - Asylbekov, Zh A.
AU - Zubov, V. N.
AU - Ulyanov, V. V.
PY - 2011/7
Y1 - 2011/7
N2 - We study the rate of weak convergence of the distributions of the statistics {tλ(Y), λ ∈ ℝ} from the power divergence family of statistics to the χ2 distribution. The statistics are constructed from n observations of a random variable with three possible values. We show that, where G2(c) is the χ2 distribution function of a random variable with two degrees of freedom. In the proof we use Huxley's theorem of 1993 on approximating the number of integer points in a plane convex set with smooth boundary by the area of the set.
AB - We study the rate of weak convergence of the distributions of the statistics {tλ(Y), λ ∈ ℝ} from the power divergence family of statistics to the χ2 distribution. The statistics are constructed from n observations of a random variable with three possible values. We show that, where G2(c) is the χ2 distribution function of a random variable with two degrees of freedom. In the proof we use Huxley's theorem of 1993 on approximating the number of integer points in a plane convex set with smooth boundary by the area of the set.
KW - accuracy of χ approximation
KW - Huxley theorem
KW - integer points
KW - power divergence family of statistics
UR - http://www.scopus.com/inward/record.url?scp=80051991971&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80051991971&partnerID=8YFLogxK
U2 - 10.1134/S0037446611040021
DO - 10.1134/S0037446611040021
M3 - Article
VL - 52
SP - 571
EP - 584
JO - Siberian Mathematical Journal
JF - Siberian Mathematical Journal
SN - 0037-4466
IS - 4
ER -