# Lin'kov Yu. N.

### Properties of the Likelihood Ratio for Counting Processes in the Problem of Estimation of Unknown Parameters

Lin'kov Yu. N., Nikolaeva O. A.

Ukr. Mat. Zh. - 2000. - 52, № 9. - pp. 1257-1268

We obtain an asymptotic decomposition of the logarithm of the likelihood ratio for counting processes in the case of similar hypotheses. We establish the properties of the normalized likelihood ratio in the problem of estimation of an unknown parameter.

### Large deviations for Bayes discrimination of a finite number of simple hypotheses

Gabriel' L. A., Lin'kov Yu. N.

Ukr. Mat. Zh. - 1999. - 51, № 10. - pp. 1360–1367

We consider the problem of discrimination of a finite number of simple hypotheses in the general scheme of statistical experiments. Under conditions of the validity of theorems on large deviations for the logarithm of likelihood ratio, we investigate the asymptotic behavior of probabilities of errors of the Bayes criterion. We obtain the asymptotics of the amount of Shannon information contained in an observation and in the Bayes criterion.

### Properties of the likelihood ratio for semimartingales with deterministic triplets in the parametric case

Lin'kov Yu. N., Shevlyakov A. Yu.

Ukr. Mat. Zh. - 1999. - 51, № 9. - pp. 1172–1180

We consider semimartingales with deterministic discontinuous triplets. We obtain properties of the like-lihood ratio for the parametric case in terms of the Hellinger processes.

### Asymptotic distinguishing of autoregressive processes

Ukr. Mat. Zh. - 1996. - 48, № 5. - pp. 635-641

We study the behavior of the probability of errors of the Neumann-Pearson criterion under various null and alternative hypotheses by the results of observations of autoregressive processes.

### Large deviation theorems in the problem of testing two simple hypotheses

Lin'kov Yu. N., Medvedeva M. I.

Ukr. Mat. Zh. - 1995. - 47, № 2. - pp. 227–235

Limit theorems on large deviations of the logarithm of the likelihood ratio are proved for the problem of distinguishing two simple hypotheses in the general scheme of statistical experiments under the null hypothesis and under an alternative hypothesis. The theorems obtained are applied to the investigation of a decrease in the probability of errors of the first and second kind for the Neumann-Pearson criterion.

### Large deviations in the problem of distinguishing the counting processes

Ukr. Mat. Zh. - 1993. - 45, № 11. - pp. 1514–1521

We prove the general limit theorem on probability of large deviations of the logarithm of the likelihood ratio with the null hypothesis and alternative. Weaker versions of the principle of large deviations are obtained in predictable terms for the problem of distinguishing the counting processes. The case of counting processes with deterministic compensators is studied.

### Asymptotic distinction of counting processes

Ukr. Mat. Zh. - 1993. - 45, № 7. - pp. 972–979

A canonical representation is obtained for the logarithm of the likelihood ratio. Limit theorems describing its asymptotic behavior are proved. Using these theorems, we study the rate of decrease of the probability of an error of the second-kind in the Neyman-Pearson test.