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 Diskr. Mat., 2009, Volume 21, Issue 2, Pages 126–137 (Mi dm1052)

On a class of statistics of polynomial samples

B. I. Selivanov

Abstract: We consider $M\ge1$ independent samples each of which is a realisation of some polynomial scheme. The number of outcomes $N$ and the number of samples $M$ are fixed, the sample sizes grow without bound. We study the asymptotic properties of statistics of the form $g(\overline\xi)$, where $g(\overline\xi)$ is a differentiable function of $MN$ real-valued variables, is the vector of relative frequencies of outcomes in samples. Statistics of such a kind are playing an important part in the applied statistical analysis.
In this research we expand the capabilities of the well-known $\delta$-method (the linearisation method) in the case of polynomial samples. We prove the asymptotic normality and convergence in distribution of the statistics $g(\overline\xi)$ to quadratic forms of normal random variables (both for the fixed probabilities of outcomes in the case of the null hypothesis and for the case of contigual alternatives to it). We give conditions for both types of convergence.

DOI: https://doi.org/10.4213/dm1052

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English version:
Discrete Mathematics and Applications, 2009, 19:3, 309–320

Bibliographic databases:

Document Type: Article
UDC: 519.2

Citation: B. I. Selivanov, “On a class of statistics of polynomial samples”, Diskr. Mat., 21:2 (2009), 126–137; Discrete Math. Appl., 19:3 (2009), 309–320

Citation in format AMSBIB
\Bibitem{Sel09} \by B.~I.~Selivanov \paper On a~class of statistics of polynomial samples \jour Diskr. Mat. \yr 2009 \vol 21 \issue 2 \pages 126--137 \mathnet{http://mi.mathnet.ru/dm1052} \crossref{https://doi.org/10.4213/dm1052} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2562233} \elib{http://elibrary.ru/item.asp?id=20730292} \transl \jour Discrete Math. Appl. \yr 2009 \vol 19 \issue 3 \pages 309--320 \crossref{https://doi.org/10.1515/DMA.2009.019} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67849118550} 

• http://mi.mathnet.ru/eng/dm1052
• https://doi.org/10.4213/dm1052
• http://mi.mathnet.ru/eng/dm/v21/i2/p126

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. A. M. Zubkov, B. I. Selivanov, “On a statistic for testing the homogeneity of polynomial samples”, Discrete Math. Appl., 25:2 (2015), 109–120
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