The Information Inequality in Sequential Estimation for the Uniform Case

Masafumi Akahira; Kei Takeuchi

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The Information Inequality in Sequential Estimation for the Uniform Case

机译：一致情况下顺序估计中的信息不等式

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摘要

We consider sequential estimation of a parameter based on the independent and identically distributed sample from the uniform distribution with range 1. The optimal sequential estimation procedure in the sense of minimizing the Bayes risk with respect to the uniform prior distribution is obtained, from which the information inequality derived. A comparison between the sequential and nonsequential cases is also given.

机译：我们考虑从范围为1的均匀分布中，基于独立且分布均匀的样本对参数进行顺序估计。从最小化相对于均匀先验分布的贝叶斯风险的角度出发，获得了最佳顺序估计过程，从该过程中可以获得信息不平等的产生。还给出了顺序情况和非顺序情况之间的比较。

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来源
《Sequential analysis》 |2003年第3期|p.223-232|共10页
作者
Masafumi Akahira; Kei Takeuchi;
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作者单位

Institute of Mathematics, University of Tsukuba, Ibaraki 305-8571, Japan;

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原文格式 PDF
正文语种 eng
中图分类统计学;
关键词
uniform distributions; sequential estimation procedure; bayes risk; prior distribution; posterior distribution; stopping timer; information inequality;

机译：均匀分布;顺序估计程序;贝叶斯风险;先验分布;后验分布;停止计时器;信息不平等;

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1. AN ESTIMATE OF THE ABSOLUTE CONSTANT IN THE INEQUALITY FOR THE UNIFORM DISTANCE BETWEEN THE DISTRIBUTIONS OF SEQUENTIAL SUMS OF INDEPENDENT RANDOM VARIABLES [J] . E. L. Maistrenko Journal of Mathematical Sciences . 2018,第6期

机译：独立随机变量序列和分布的均匀距离不等式中的绝对常数的一个估计
2. ON SEQUENTIAL POINT ESTIMATION IN A UNIFORM DISTRIBUTION WITH ADJUSTED NON-SUFFICIENT ESTIMATORS: A COMPARATIVE STUDY AND REAL DATA ILLUSTRATION [J] . DEBANJAN BHATTACHARJEE, NITIS MUKHOPADHYAY Calcutta statistical association bulletin . 2013,第257a260期

机译：调整后的非充分估计均匀分布中的序列点估计：比较研究和实数据说明
3. Sequential Interval Estimation of a Location Parameter with the Fixed Width in the Uniform Distribution with an Unknown Scale Parameter [J] . Masafumi Akahira, Ken-ichi Koike Sequential analysis . 2005,第1期

机译：尺度参数未知的均匀分布中具有固定宽度的位置参数的顺序区间估计
4. Sequential Inverse Covariance Intersection Fusion Estimation for Non-uniform Sampling Systems with Fading Measurements [C] . Honglei LIN, Shuli SUN Chinese Control Conference . 2020

机译：具有衰减测量的非均匀采样系统的顺序逆协方差相交融合估计
5. SEQUENTIAL AND NON-SEQUENTIAL CONFIDENCE INTERVALS WITH GUARANTEED COVERAGE PROBABILITY AND BETA-PROTECTION (ESTIMATION, STATISTICS, MINIMAXITY). [D] . JUHLIN, KENTON DUANE. 1985

机译：顺序和非顺序置信区间，具有保证的覆盖概率和Beta保护（估计，统计，最小限度）。
6. DYNAMIC PROGRAMMING SEQUENTIAL ESTIMATION AND SEQUENTIAL DETECTION PROCESSES [O] . Richard Bellman, Robert Kalaba, David Middleton 1961

机译：动态编程顺序估计和顺序检测过程
7. Two-stage sequential estimation procedures for the uniform distribution(Sequential Analysis and Statistical Inference) [O] . 赤平昌文 1993

机译：均匀分布的两阶段顺序估计程序（顺序分析和统计推断）
8. Sequential Estimation in the Uniform Density [R] . Cooke, P. J. 1969

机译：均匀密度下的序贯估计

The Information Inequality in Sequential Estimation for the Uniform Case

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