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BSU bulletin. Mathematics, Informatics

Bibliographic description:
Mezhennaya N. M.
ABOUT TESTING THE DENSE EMBEDDING HYPOTHESIS FOR DISCRETE RANDOM SEQUENCES // BSU bulletin. Mathematics, Informatics. - 2017. №4. . - С. 9-20.
Title:
ABOUT TESTING THE DENSE EMBEDDING HYPOTHESIS FOR DISCRETE RANDOM SEQUENCES
Financing:
Codes:
DOI: 10.18101/2304-5728-2017-4-9-20UDK: 519.226, 519.244.3, 519.244.8
Annotation:
The dense embedding hypothesis says that one discrete sequence can be embedded in the other in such a way that the characters of the inserted se- quence are separated in the resulting sequence by at most one character. We propose a sequential test for the dense imbedding hypothesis for discrete equiprobable random sequences over a finite alphabet and study its properties. The probability of type I error (the probability of rejection of the dense embed- ding hypothesis when it’s true) of the constructed test equals zero. We derive an expression for the probability of type II error under the alternative hypothe- sis that the discrete sequences under consideration are independent. A class of similar test is also considered. It turns out that a small change in the testing procedure greatly changes the error probabilities. A numerical illustration and discussion of the results are given.
Keywords:
dense embedding; sequential test; hypothesis of independence; probabilities of type I and type II errors; discrete random sequence.
List of references: