On properties of the likelihood function in the problem of estimation of the instants of changes of the success probability in nonhomogeneous Bernoulli trials
Diskretnaya Matematika, Tome 22 (2010) no. 2, pp. 60-65
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M. I. Tikhomirova; V. P. Chistyakov. On properties of the likelihood function in the problem of estimation of the instants of changes of the success probability in nonhomogeneous Bernoulli trials. Diskretnaya Matematika, Tome 22 (2010) no. 2, pp. 60-65. http://geodesic.mathdoc.fr/item/DM_2010_22_2_a4/
@article{DM_2010_22_2_a4,
author = {M. I. Tikhomirova and V. P. Chistyakov},
title = {On properties of the likelihood function in the problem of estimation of the instants of changes of the success probability in nonhomogeneous {Bernoulli} trials},
journal = {Diskretnaya Matematika},
pages = {60--65},
year = {2010},
volume = {22},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DM_2010_22_2_a4/}
}
TY - JOUR
AU - M. I. Tikhomirova
AU - V. P. Chistyakov
TI - On properties of the likelihood function in the problem of estimation of the instants of changes of the success probability in nonhomogeneous Bernoulli trials
JO - Diskretnaya Matematika
PY - 2010
SP - 60
EP - 65
VL - 22
IS - 2
UR - http://geodesic.mathdoc.fr/item/DM_2010_22_2_a4/
LA - ru
ID - DM_2010_22_2_a4
ER -
%0 Journal Article
%A M. I. Tikhomirova
%A V. P. Chistyakov
%T On properties of the likelihood function in the problem of estimation of the instants of changes of the success probability in nonhomogeneous Bernoulli trials
%J Diskretnaya Matematika
%D 2010
%P 60-65
%V 22
%N 2
%U http://geodesic.mathdoc.fr/item/DM_2010_22_2_a4/
%G ru
%F DM_2010_22_2_a4
We obtain the expression of the statistic which is a linear function of the logarithm of the likelihood function and investigate properties of the mathematical expectation of this function. The results obtained can be applied to the estimation of instants of changes of the success probability in Bernoulli trials.
[1] Borovkov A. A., “Asimptoticheski optimalnye resheniya v zadache o razladke”, Teoriya veroyatnostei i ee primeneniya, 43:4 (1998), 623–654 | MR | Zbl
[2] Darkhovskii B. S., “Neparametricheskii metod otsenivaniya intervalov odnorodnosti sluchainoi posledovatelnosti”, Teoriya veroyatnostei i ee primeneniya, 30:4 (1985), 795–799 | MR | Zbl
[3] Hinkley D. V., Hinkley E. A., “Inference about the change-point in a sequence of binomial variables”, Biometrika, 57:3 (1970), 477–488 | DOI | MR | Zbl
[5] Zubkov A. M., Sokolov D. V., “Statistical inference for noisy piecewise linear signals”, Dokl. 1-i Mezhd. konf. “Tsifrovaya obrabotka signalov i ee primeneniya”, v. II-E, Moskva, 1998, 140–142
[6] Brodskii B. E., Darkhovskii B. S., “Problemy i metody veroyatnostnoi diagnostiki”, Avtomatika i telemekhanika, 8 (1999), 3–50 | MR | Zbl