Author | Akahira, Masafumi. author |
---|---|
Title | Asymptotic Efficiency of Statistical Estimators: Concepts and Higher Order Asymptotic Efficiency [electronic resource] / by Masafumi Akahira, Kei Takeuchi |
Imprint | New York, NY : Springer New York, 1981 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-5927-5 |
Descript | 242 p. online resource |
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 Xiโs 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