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 |
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Pages (from-to) | 571-584 |
Number of pages | 14 |
Journal | Siberian Mathematical Journal |
Volume | 52 |
Issue number | 4 |
DOIs | |
Publication status | Published - Jul 2011 |
Keywords
- Huxley theorem
- accuracy of χ approximation
- integer points
- power divergence family of statistics
ASJC Scopus subject areas
- Mathematics(all)