1. General discussions on unbiased estimation. - 1. 1. Formulation. - 1. 2. Undominated case. - 1. 3. The support depending on the parameter. - 1. 4. Discrete parameter set. - 1. 5. Discontinuous and non-differentiable density. - 1. 6. Non square-integrable likelihood ratio. - 1. 7. Asymptotic theory for non-regular cases. - 1. 8. Asymptotic Bayes posterior distribution of the parameter in non-regular cases. - 1. 9. Overview. - 2. Lower bound for the variance of unbiased estimators. - 2. 1. Minimum variance. - 2. 2. Bhattacharyya type bound for the variance of unbiased estimators in non-regular cases. - 2. 3. Lower bound for the variance of unbiased estimators for one-directional distributions. - 2. 4. A second type of one-directional distribution and the lower bound for the variance of unbiased estimators. - 2. 5. Locally minimum variance unbiased estimation. - 3. Amounts of information and the minimum variance unbiased estimation. - 3. 1. Fisher information and the minimum variance unbiased estimation. - 3. 2. Examples on unbiased estimators with zero variance. - 3. 3. A definition of the generalized amount of information. - 3. 4. Examples on the generalized amount of information. - 3. 5. Order of consistency. - 4. Loss of information associated with the order statistics and related estimators in the case of double exponential distributions. - 4. 1. Loss of information of the order statistics. - 4. 2. The asymptotic loss of information. - 4. 3. Proofs of Theorems in Section 4. 2. - 4. 4. Discretized likelihood estimation. - 4. 5. Second order asymptotic comparison of the discretized likelihood estimator with others. - 5. Estimation of a common parameter for pooled samples from the uniform distributions and the double exponential distributions. - 5. 1. Estimators of a common parameter for the uniform distributions. - 5. 2. Comparison of the quasi-MLE the weighted estimator and others for the uniform distributions. - 5. 3. Estimators of a common parameter for the double exponential distributions. - 5. 4. Second order asymptotic comparison of the estimators for the double exponential distributions. - 6. Higher order asymptotics in estimation for two-sided Weibull type distributions. - 6. 1. The 2?-th order asymptotic bound for the distribution of 2?-th order AMU estimators. - 6. 2. Proofs of Lemmas and Theorem in Section 6. 1. - 6. 3. The 2?-th order asymptotic distribution of the maximum likelihood estimator. - 6. 4. The amount of the loss of asymptotic information of the maximum likelihood estimator. - 7. 3/2-th and second order asymptotics of the generalized Bayes estimators for a family of truncated distributions. - 7. 1. Definitions and assumptions. - 7. 2. Generalized Bayes estimators for a family of truncated distributions. - 7. 3. Second order asymptotic bound in symmetrically truncated densities. - 7. 4. Maximum probability estimation. - 7. 5. Examples. - 7. 6. Some remarks. - Supplement. The bound for the asymptotic distribution of estimators when the maximum order of consistency depends on the parameter. - 5. 1. Order of consistency depending on the parameter. - 5. 2. The bound for the asymptotic distribution of AMU estimators in the autoregressive process. - References. Language: English