Geometrical theory of higher-order asymptotics of test, interval estimator and conditional inference
Geometrical theory of higher-order asymptotics of test, interval estimator and conditional inference
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检验、区间估计和条件推理的高阶渐近几何理论
DOI：
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发表时间：
1983
期刊：
影响因子：
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通讯作者：
S. Amari
中科院分区：
文献类型：
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作者：
M. Kumon;S. Amari
本文利用微分几何的概念，对单参数曲指数分布族的单侧和双侧检验的高阶渐近幂进行了条件和无条件的估计。高阶渐近功率和期望大小的单侧和双侧区间估计，条件和无条件的，也得到了。借助近似辅助统计量，设计了在任意指定点处均为三阶最强的检验和区间估计。通过证明条件推理与似然比推理在三阶以下的等价性，阐明了条件推理的特征。几何概念，如曲率和角度在本理论中起着基本的作用。
Higher order asymptotic powers of one-sided and two-sided tests, both conditional and unconditional, are evaluated for a one-parameter curved exponential family of distributions by using differential-geometrical notions. Higher order asymptotic powers and the expected size of one-sided and two-sided interval estimators, both conditional and unconditional, are also obtained. The tests and interval estimators, which are third-order most powerful at any arbitrary specified one point are explicitly designed with the help of the approximate ancillary statistic. The characteristics of the conditional inference are elucidated, by proving the equivalence up to the third order of the conditional inference and likelihood ratio inference. Geometrical notions such as curvatures and angles play a fundamental role in the present theory.