Matches in Library of Congress for { ?s ?p Machine generated contents note: Chapter 1. Local Densities of Measures and Limit Theorems for Stochastic -- Processes 1 -- 1.1. Basic notions of the theory of stochastic processes 1 -- 1.2. Statistic experiments generated by stochastic processes 9 -- 1.3. Limit theorems for semimartingales 21 -- Chapter 2. Asymptotic Distinguishing between Simple Hypotheses in the -- Scheme of General Statistical Experiments 33 -- 2.1. Statistical hypotheses and tests 33 -- 2.2. Types of asymptotic distinguishability between families of hypothe- -- ses and their characterization 36 -- 2.3. Complete asymptotic distinguishability under the conditions of the -- law of large numbers 45 -- 2.4. Complete asymptotic distinguishability under conditions of weak -- convergence 52 -- 2.5. Contiguous families of hypotheses 58 -- 2.6. The case of asymptotic expansion of the likelihood ratio 65 -- 2.7. Reduction of the problem of testing hypotheses 70 -- Chapter 3. Asymptotic Behavior of the Likelihood Ratio in Problems of -- Distinguishing between Simple Hypotheses for Semimartingales 79 -- 3.1. Hellinger integrals and Hellinger processes 79 -- 3.2. Limit theorems for'the likelihood ratio 83 -- 3.3. Asymptotic decomposition of the likelihood ratio in parametric -- formulation 88 -- 3.4. Observations of diffusion-type processes 98 -- 3.5. Observations of counting processes 112 -- Chapter 4. Asymptotic Estimation of Parameters 137 -- 4.1. Formulation of the problem 137 -- 4.2. Properties of the normalized likelihood ratio for semimartingales 140 -- 4.3. Observations of diffusion-type processes 151 -- 4.4. Observations of counting processes 156 -- Chapter 5. Asymptotic Information-Theoretic Problems in Parameter Es- -- timation 161 -- 5.1. Asymptotic behavior of the Shannon information in observations -- with respect to an unknown parameter 161 -- 5.2. Lower bounds for the information about a statistical estimate of a -- parameter 174 -- 5.3. Bounds for risk functions of consistent estimates 186 -- 5.4. Observations of semimartingales 194 -- Bibliographical Notes 197 -- References 203 -- Index 213.. }
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- 00045349 description "Machine generated contents note: Chapter 1. Local Densities of Measures and Limit Theorems for Stochastic -- Processes 1 -- 1.1. Basic notions of the theory of stochastic processes 1 -- 1.2. Statistic experiments generated by stochastic processes 9 -- 1.3. Limit theorems for semimartingales 21 -- Chapter 2. Asymptotic Distinguishing between Simple Hypotheses in the -- Scheme of General Statistical Experiments 33 -- 2.1. Statistical hypotheses and tests 33 -- 2.2. Types of asymptotic distinguishability between families of hypothe- -- ses and their characterization 36 -- 2.3. Complete asymptotic distinguishability under the conditions of the -- law of large numbers 45 -- 2.4. Complete asymptotic distinguishability under conditions of weak -- convergence 52 -- 2.5. Contiguous families of hypotheses 58 -- 2.6. The case of asymptotic expansion of the likelihood ratio 65 -- 2.7. Reduction of the problem of testing hypotheses 70 -- Chapter 3. Asymptotic Behavior of the Likelihood Ratio in Problems of -- Distinguishing between Simple Hypotheses for Semimartingales 79 -- 3.1. Hellinger integrals and Hellinger processes 79 -- 3.2. Limit theorems for'the likelihood ratio 83 -- 3.3. Asymptotic decomposition of the likelihood ratio in parametric -- formulation 88 -- 3.4. Observations of diffusion-type processes 98 -- 3.5. Observations of counting processes 112 -- Chapter 4. Asymptotic Estimation of Parameters 137 -- 4.1. Formulation of the problem 137 -- 4.2. Properties of the normalized likelihood ratio for semimartingales 140 -- 4.3. Observations of diffusion-type processes 151 -- 4.4. Observations of counting processes 156 -- Chapter 5. Asymptotic Information-Theoretic Problems in Parameter Es- -- timation 161 -- 5.1. Asymptotic behavior of the Shannon information in observations -- with respect to an unknown parameter 161 -- 5.2. Lower bounds for the information about a statistical estimate of a -- parameter 174 -- 5.3. Bounds for risk functions of consistent estimates 186 -- 5.4. Observations of semimartingales 194 -- Bibliographical Notes 197 -- References 203 -- Index 213.".
- 00045349 tableOfContents "Machine generated contents note: Chapter 1. Local Densities of Measures and Limit Theorems for Stochastic -- Processes 1 -- 1.1. Basic notions of the theory of stochastic processes 1 -- 1.2. Statistic experiments generated by stochastic processes 9 -- 1.3. Limit theorems for semimartingales 21 -- Chapter 2. Asymptotic Distinguishing between Simple Hypotheses in the -- Scheme of General Statistical Experiments 33 -- 2.1. Statistical hypotheses and tests 33 -- 2.2. Types of asymptotic distinguishability between families of hypothe- -- ses and their characterization 36 -- 2.3. Complete asymptotic distinguishability under the conditions of the -- law of large numbers 45 -- 2.4. Complete asymptotic distinguishability under conditions of weak -- convergence 52 -- 2.5. Contiguous families of hypotheses 58 -- 2.6. The case of asymptotic expansion of the likelihood ratio 65 -- 2.7. Reduction of the problem of testing hypotheses 70 -- Chapter 3. Asymptotic Behavior of the Likelihood Ratio in Problems of -- Distinguishing between Simple Hypotheses for Semimartingales 79 -- 3.1. Hellinger integrals and Hellinger processes 79 -- 3.2. Limit theorems for'the likelihood ratio 83 -- 3.3. Asymptotic decomposition of the likelihood ratio in parametric -- formulation 88 -- 3.4. Observations of diffusion-type processes 98 -- 3.5. Observations of counting processes 112 -- Chapter 4. Asymptotic Estimation of Parameters 137 -- 4.1. Formulation of the problem 137 -- 4.2. Properties of the normalized likelihood ratio for semimartingales 140 -- 4.3. Observations of diffusion-type processes 151 -- 4.4. Observations of counting processes 156 -- Chapter 5. Asymptotic Information-Theoretic Problems in Parameter Es- -- timation 161 -- 5.1. Asymptotic behavior of the Shannon information in observations -- with respect to an unknown parameter 161 -- 5.2. Lower bounds for the information about a statistical estimate of a -- parameter 174 -- 5.3. Bounds for risk functions of consistent estimates 186 -- 5.4. Observations of semimartingales 194 -- Bibliographical Notes 197 -- References 203 -- Index 213.".