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Teoriya Veroyatnostei i ee Primeneniya, 1977, Volume 22, Issue 1, Pages 106–121
(Mi tvp3105)
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This article is cited in 9 scientific papers (total in 9 papers)
Tests of composite hypotheses for random variables and random processes
K. O. Džaparidze Tbilisi
Abstract:
Let a sequence of random variables $X(t)$, $t=\dots,-1,0,1,\dots$, or of a random process $X(t)$, $-\infty<t<\infty$, be observed at $t=1,\dots,T$ or $0\le t\le T$. The general problem is considered of testing composite hypotheses for probability distributions of $X(t)$ on the basis of observations. Two different tests are proposed, and it is shown that the asymptotic properties of both these tests coincide quite often with the asymptotic properties of the likelihood-ratio test. It is also shown that the proposed tests generalize many previously known tests. The special case of Gaussian and stationary $X(t)$ is studied.
Received: 24.07.1975
Citation:
K. O. Džaparidze, “Tests of composite hypotheses for random variables and random processes”, Teor. Veroyatnost. i Primenen., 22:1 (1977), 106–121; Theory Probab. Appl., 22:1 (1977), 104–118
Linking options:
https://www.mathnet.ru/eng/tvp3105 https://www.mathnet.ru/eng/tvp/v22/i1/p106
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