在统计学中,巴苏定理(Basu's Theorem)指出任何有界完全的充分统计量与任何辅助统计量独立。这是Debabrata Basu于1955年发现的结论。 设{\displaystyle P_{\theta }} 1, 2,...,是独立同分布的正态分布随机变量,其中方差{\displaystyle \sigma ^{2}}可以证明样本均值 是充分完全统计量,并且样本方差 是辅助统计...
在统计学领域，巴苏定理（Basu's Theorem）揭示了一个重要的统计特性，即任何有界完全的充分统计量与任何辅助统计量独立。这一结论由Debabrata Basu在1955年提出。设为一可测空间上的分布族。如果T是的充分且有界完全的统计量，A是关于的辅助统计量，那么T与A独立。具体而言，对于任意博雷尔集B，构造函数...
写本文的原因是因为不满教科书内的Basu‘s Theorem证明和完备统计量的定义都太过不直观,因此本文尝试用非常直观的方式来理解为什么我们需要定义“完备性”,以及Basu‘s Theorem到底在说什么。(真无语我到phd才…
Basu's theorem (Basu (1955)) says that a boundedly complete sufficient statistic and any ancillary statistics are independently distributed under all 胃 . This is Theorem 2 in the paper. This was Basu's first paper on sufficiency, and arguably the most well known. Numerous applications of ...
This article reviews some basic ideas of classical inference and the roles they play in Basu's theorem. The usefulness of this theorem is demonstrated by applications to various statistical problems.doi:10.2307/2685927Dennis D. Boos and Jacqueline M. Hughes-Oliver...
Theorem 1, part b) can be used to say that, when the sampling fraction f = n/N is negligible, one can avoid actually performing simulations and approximate the posterior distri- bution with the Dirichlet distribution. This idea is crucial in the development of Polya's Posterior methodology, ...
Think CAP theorem. This is a distributed system, network partition will occur, be explicit about your availability and consistency model in that event All remote calls will fail, have re-tries that uses exponential back-off. Log warning on re-tries and error if it finally fails Ensure we alw...
Basu's theoremCompletenessConditioningUnbiased estimationIn order to obtain a statistical interpretation of completeness of a sufficient statistic T, an attempt is made to characterize this property as equivalent to the condition that all ancillary statistics are independent of T. For technical reasons, ...
World Bank economist Kaushik Basu proves Pythagorean Theorem (2,600 years late)Peter Coy