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Teoriya Veroyatnostei i ee Primeneniya, 1977, Volume 22, Issue 1, Pages 3–17
(Mi tvp3098)
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This article is cited in 28 scientific papers (total in 28 papers)
Decomposable statistics in a polynomial scheme. I
Yu. I. Medvedev Moscow
Abstract:
Let a random vector $\nu=(\nu_1,\nu_2,\dots,\nu_N)$ have the polynomial distribution with
parameters $n$; $p_1,p_2,\dots,p_N$. A random variable $\displaystyle L(\nu)=\sum_{m=1}^N f_m(\nu_m)$, where $f_1(x),f_2(x),\dots,f_N(x)$ are arbitrary given functions, is called a decomposable statistic.
The paper deals with the limiting laws of the distribution of decomposable statistics as $n$, $N\to\infty$ for small samples, i. e. when $\displaystyle\max_m np_m\le c<\infty$, and under some weak constraints on functions $f_m(x)$. The class of decomposable statistics includes statistic $\chi^2$, likelihood ratios, linear combinations of random variables $\mu_r$, where $\mu_r$ is the number of the coordinates of $\nu$ equal to $r$, and others.
Received: 15.05.1975
Citation:
Yu. I. Medvedev, “Decomposable statistics in a polynomial scheme. I”, Teor. Veroyatnost. i Primenen., 22:1 (1977), 3–17; Theory Probab. Appl., 22:1 (1977), 1–15
Linking options:
https://www.mathnet.ru/eng/tvp3098 https://www.mathnet.ru/eng/tvp/v22/i1/p3
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Abstract page: | 309 | Full-text PDF : | 144 |
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