Joint Statistical Papers of Akahira and Takeuchi Book

	Foreword
	Introduction
1	Characterizations of Prediction Sufficiency (Adequacy) in terms of Risk Functions	1
2	On the Second Order Asymptotic Efficiency of Estimators in Multiparameter Cases	8
3	On Gram-Charlier-Edgeworth Type Expansion of the Sums of Random Variables (I)	17
4	On Gram-Charlier-Edgeworth Type Expansion of the Sums of Random Variables (II)	38
5	On the Second Order Asymptotic Efficiencies of Estimators	45
6	Extension of Edgeworth Type Expansion of the Distribution of the Sums of I.I.D. Random Variables in Non-Regular Cases	80
7	On Gram-Charlier-Edgeworth Type Expansion of the Sums of Random Variables (III) Multivariate Cases	90
8	Third Order Asymptotic Efficiency of Maximum Likelihood Estimator for Multiparameter Exponential Case	101
9	Asymptotic Optimality of the Generalized Bayes Estimator	124
10	On the Second Order Asymptotic Efficiency of Unbiased Confidence Intervals	133
11	Remarks on the Asymptotic Efficiency and Inefficiency of Maximum Probability Estimators	145
12	Discretized Likelihood Methods - Asymptotic Properties of Discretized Likelihood Estimators (DLE's)	152
13	Asymptotic Optimality of the Generalized Bayes Estimator in Multiparameter Cases	170
14	Note on Non-Regular Asymptotic Estimation - What "Non-Regularity" Implies	183
15	A Note on Prediction Sufficiency (Adequacy) and Sufficiency	187
16	Third Order Asymptotic Efficiency and Asymptotic Completeness of Estimators	191
17	On Asymptotic Deficiency of Estimators in Pooled Samples in the Presence of Nuisance Parameters	199
18	Estimation of a Common Parameter for Pooled Samples from the Uniform Distributions	221
19	A Note on the Minimum Variance Unbiased Estimation When the Fisher Information is Infinity	231
20	Bhattacharyya Bound of Variances of Unbiased Estimators in Non-Regular Cases	237
21	A Note on Minimum Variance	247
22	A Note on Optimum Spacing of Observations from a Continuous Time Simple Markov Process	254
23	On the Bound of the Asymptotic Distribution of Estimators when the Maximum Order of Consistency Depends on the Parameter	260
24	On the Definition of Asymptotic Expectation	276
25	Locally Minimum Variance Unbiased Estimator in a Discontinuous Density Function	286
26	The Lower Bound for the Variance of Unbiased Estimators for One-Directional Family of Distributions	301
27	Second Order Asymptotic Efficiency in terms of Asymptotic Variances of the Sequential Maximum Likelihood Estimation Procedures	319
28	Second and Third Order Asymptotic Completeness of the Class of Estimators	325
29	Higher Order Asymptotics in Estimation for Two-sided Weibull Type Distributions	342
30	Third Order Asymptotic Efficiency of the Sequential Maximum Likelihood Estimation Procedure	370
31	First Order Asymptotic Efficiency in Semiparametric Models Implies Infinite Asymptotic Deficiency	397
32	Loss of Information Associated with the Order Statistics and Related Estimators in the Double Exponential Distribution Case	404
33	Bootstrap Method and Empirical Process	415
34	Second Order Asymptotic Efficiency in Terms of the Asymptotic Variance of Sequential Estimation Procedures in the Presence of Nuisance Parameters	429
35	Asymptotic Efficiency of Estimators for a Location Parameter Family of Densities with the Bounded Support	446
36	A Definition of Information Amount Applicable to Non-regular Cases	455
37	Unbiased Estimation in Sequential Binomial Sampling	477
38	Interval Estimation with Varying Confidence Levels	490
39	Second Order Asymptotic Bound for the Variance of Estimators for the Double Exponential Distribution	506
40	On the Application of the Minkowski-Farkas Theorem to Sampling Designs	514
41	Randomized Confidence Intervals of a Parameter for a Family of Discrete Exponential Type Distributions	517
42	The Existence of a Test with the Largest Order of Consistency in the Case of a Two-sided Gamma Type Distribution	543
43	The Higher Order Large-Deviation Approximation for the Distribution of the Sum of Independent Discrete Random Variables	558
44	Information Inequalities in a Family of Uniform Distributions	580
	Permission	589