Author(s): Linkov YU. N.
Series: Translations of mathematical monographs 196.
Publisher: American Mathematical Society
Year: 2001
Language: English
Pages: 216
City: Providence, RI
Ch. 1. Local Densities of Measures and Limit Theorems for Stochastic Processes. 1.1. Basic notions of the theory of stochastic processes. 1.2. Statistic experiments generated by stochastic processes. 1.3. Limit theorems for semimartingales --
Ch. 2. Asymptotic Distinguishing between Simple Hypotheses in the Scheme of General Statistical Experiments. 2.1. Statistical hypotheses and tests. 2.2. Types of asymptotic distinguishability between families of hypotheses and their characterization. 2.3. Complete asymptotic distinguishability under the conditions of the law of large numbers. 2.4. Complete asymptotic distinguishability under conditions of weak convergence. 2.5. Contiguous families of hypotheses. 2.6. The case of asymptotic expansion of the likelihood ratio. 2.7. Reduction of the problem of testing hypotheses --
Ch. 3. Asymptotic Behavior of the Likelihood Ratio in Problems of Distinguishing between Simple Hypotheses for Semimartingales. 3.1. Hellinger integrals and Hellinger processes. 3.2. Limit theorems for the likelihood ratio. 3.3. Asymptotic decomposition of the likelihood ratio in parametric formulation. 3.4. Observations of diffusion-type processes. 3.5. Observations of counting processes --
Ch. 4. Asymptotic Estimation of Parameters. 4.1. Formulation of the problem. 4.2. Properties of the normalized likelihood ratio for semimartingales. 4.3. Observations of diffusion-type processes. 4.4. Observations of counting processes --
Ch. 5. Asymptotic Information-Theoretic Problems in Parameter Estimation. 5.1. Asymptotic behavior of the Shannon information in observations with respect to an unknown parameter. 5.2. Lower bounds for the information about a statistical estimate of a parameter. 5.3. Bounds for risk functions of consistent estimates. 5.4. Observations of semimartingales.
