1. General discussion. - 1. 1. The concept of asymptotic efficiency. - 1. 2. Multidimensional parameter case. - 1. 3. Higher order asymptotic efficiency. - 1. 4. The estimators in the classes C and D. - 1. 5. More general cases. - 2. Consistency of estimators and order of consistency. - 2. 1. Notation and definition. - 2. 2. Necessary conditions for consistency of estimators. - 2. 3. Consistent estimators with order cn. - 2. 4. Order of convergence of cn -consistent estimators for the location parameter case. - 2. 5. Bounds for the order of convergence of consistent estimators. - 2. 6. Order of convergence of consistent estimators in an autoregressive process. - 3. Asymptotic efficiency. - 3. 1. Definitions and existence. - 3. 2. Asymptotic efficiency in an autoregressive process. - 3. 3. Asymptotic efficiency and inefficiency of maximum probability estimators. - 4. Higher order asymptotic efficiency. - 4. 1. Second order asymptotic efficiency. - 4. 2. Third order asymptotic efficiency. - 4. 3. Second order asymptotic efficiency of estimators when Xi's are not i. i. d. - 4. 4. Second order asymptotic efficiency of estimators in multiparameter cases. - 4. 5. Second order asymptotic efficiency in an autoregressive process. - 5. Second order and third order asymptotic efficiency of the maximum likelihood estimator and other esti- mators. - 5. 1. Third order asymptotic efficiency of the maximum likelihood estimator for the multiparameter exponential case. - 5. 2. Third order asymptotic efficiency of maximum likelihood estimators in general cases. - 5. 3. Second and third order asymptotic efficiency of the generalized Bayes estimator. - 5. 4. Third order asymptotic efficiency of maximum likelihood estimators in multivariate linear regression models. - 6. Discretized likelihood methods. - 6. 1. Discretized likelihood estimator(DLE). - 6. 2. Second order asymptotic efficiency of DLE. - 6. 3. Third order asymptotic efficiency of DLE. - 6. 4. Maximum log-likelihood estimator. - 6. 5. Remarks. - 7. Higher order asymptotic efficiency and asymptotic completeness. - 7. 1. The concept of asymptotic completeness of an estimator. - 7. 2. Second order asymptotic efficiency of unbiased confidence intervals. - 7. 3. Concluding remarks. - References. Language: English