This article is cited in 1 scientific paper (total in 1 paper)
On some $\chi^2$-type statistics that depend functionally on estimators of unknown parameters
M. I. Tikhomirova, V. P. Chistyakov
A series of theorems are known which state convergence of
the distributions of $\chi^2$-type statistics
based on frequencies of outcomes in a sequence of
polynomial trials to some limit distribution.
For chains of outcomes where gaps are present,
similar results are known only in the case of equiprobable outcomes.
In this paper, we extend these results to polynomial trials with arbitrary positive
probabilities of outcomes; we also study statistics resulted from
replacing the probabilities of outcomes in $\chi^2$-type statistics
by their estimators. We obtain limit distributions
of such statistics in the general case if no gaps are present, and in some special cases
otherwise. We also give a limit theorem in the case where the sequence under
consideration is a Markov chain which approaches polynomial trials.
This research was supported by the grant 1758.2003.1
of President of Russian Federation for support of leading scientific schools.
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Discrete Mathematics and Applications, 2005, 15:1, 33–46
M. I. Tikhomirova, V. P. Chistyakov, “On some $\chi^2$-type statistics that depend functionally on estimators of unknown parameters”, Diskr. Mat., 17:1 (2005), 22–34; Discrete Math. Appl., 15:1 (2005), 33–46
Citation in format AMSBIB
\by M.~I.~Tikhomirova, V.~P.~Chistyakov
\paper On some $\chi^2$-type statistics that depend functionally on estimators of unknown parameters
\jour Diskr. Mat.
\jour Discrete Math. Appl.
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This publication is cited in the following articles:
M. I. Tikhomirova, “Some characteristics of dependencies in discrete random sequences”, Discrete Math. Appl., 18:2 (2008), 173–180
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