Tests of composite hypotheses for random variables and random processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 1, pp. 106-121
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Let a sequence of random variables $X(t)$, $t=\dots,-1,0,1,\dots$, or of a random process $X(t)$, $-\infty$, 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.
@article{TVP_1977_22_1_a7,
author = {K. O. D\v{z}aparidze},
title = {Tests of composite hypotheses for random variables and random processes},
journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
pages = {106--121},
publisher = {mathdoc},
volume = {22},
number = {1},
year = {1977},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TVP_1977_22_1_a7/}
}
K. O. Džaparidze. Tests of composite hypotheses for random variables and random processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 22 (1977) no. 1, pp. 106-121. http://geodesic.mathdoc.fr/item/TVP_1977_22_1_a7/