minimal ancillary statistic

简明释义

最小辅助统计量

英英释义

例句

1.When designing experiments, one should consider the role of the minimal ancillary statistic 最小辅助统计量 in ensuring unbiased results.

在设计实验时，应考虑最小辅助统计量在确保无偏结果中的作用。

2.Understanding the properties of a minimal ancillary statistic 最小辅助统计量 can lead to better statistical inference.

理解最小辅助统计量的性质可以导致更好的统计推断。

3.The statistical model was refined by incorporating a minimal ancillary statistic 最小辅助统计量 to account for additional variability.

通过引入最小辅助统计量来考虑额外的变异性，统计模型得到了改进。

4.The researcher found that the minimal ancillary statistic 最小辅助统计量 helped to reduce the variance in their estimates.

研究人员发现，最小辅助统计量有助于减少他们估计的方差。

5.In the context of hypothesis testing, using a minimal ancillary statistic 最小辅助统计量 can simplify the decision-making process.

在假设检验的背景下，使用一个最小辅助统计量可以简化决策过程。

作文

In the realm of statistics, the concept of a minimal ancillary statistic is crucial for understanding the behavior of estimators and the efficiency of statistical procedures. An ancillary statistic is a statistic that provides information about the sample but does not provide any information about the parameter being estimated. Specifically, a minimal ancillary statistic is one that retains all the information contained in the ancillary statistics while being as simple as possible. This concept is particularly important in the context of sufficiency and completeness in statistical inference.To illustrate the importance of a minimal ancillary statistic, consider a scenario where we are estimating the mean of a normally distributed population. In this case, the sample mean itself is a sufficient statistic for the mean, but it can also be accompanied by other statistics, such as the sample variance, which may not be necessary for the estimation of the mean. However, if we identify a minimal ancillary statistic, we can simplify our analysis and focus only on the essential components that contribute to our understanding of the data.The beauty of using a minimal ancillary statistic lies in its ability to reduce complexity without sacrificing the richness of the information it conveys. For instance, in many applications, researchers may encounter multiple ancillary statistics that seem relevant. By distilling these down to a minimal ancillary statistic, they can streamline their analyses, making it easier to communicate results and conclusions.Moreover, the identification of a minimal ancillary statistic can lead to more robust statistical methods. When dealing with large datasets or complex models, having a simplified statistic can enhance computational efficiency. This is especially valuable in fields like machine learning and data science, where algorithms often require optimization over numerous parameters. By focusing on a minimal ancillary statistic, practitioners can achieve faster convergence and improved model performance.In addition, the concept of a minimal ancillary statistic can also play a significant role in hypothesis testing. When formulating null and alternative hypotheses, it is critical to base decisions on the most relevant information. Utilizing a minimal ancillary statistic ensures that the tests are grounded in the most pertinent data, thereby increasing the reliability of the results. This can prevent misleading conclusions that might arise from considering extraneous information.Furthermore, the study of minimal ancillary statistics can foster deeper insights into the underlying structure of the data. By focusing on the minimal aspects that still capture the essence of the dataset, statisticians can uncover patterns and relationships that may not be apparent when analyzing the full set of ancillary statistics. This can lead to new discoveries and advancements in various fields of research.In conclusion, the concept of a minimal ancillary statistic is an essential tool in the field of statistics. It allows researchers to simplify their analyses, enhance computational efficiency, improve hypothesis testing, and gain deeper insights into their data. As statisticians continue to refine their methods and approaches, the importance of identifying and utilizing minimal ancillary statistics cannot be overstated. Embracing this concept will undoubtedly lead to more effective and insightful statistical practices in the future.

在统计学领域，最小附属统计量的概念对于理解估计量的行为和统计程序的效率至关重要。附属统计量是提供关于样本信息但不提供关于被估计参数信息的统计量。具体来说，最小附属统计量是保留所有附属统计量所包含的信息，同时尽可能简单的统计量。这个概念在统计推断的充分性和完整性背景下尤为重要。为了说明最小附属统计量的重要性，考虑一个我们正在估计正态分布总体均值的场景。在这种情况下，样本均值本身是均值的充分统计量，但它也可以伴随其他统计量，如样本方差，这可能对均值的估计并不是必要的。然而，如果我们识别出一个最小附属统计量，我们可以简化我们的分析，专注于对我们理解数据有贡献的基本组成部分。使用最小附属统计量的美妙之处在于，它能够在不牺牲其所传达信息的丰富性的情况下减少复杂性。例如，在许多应用中，研究人员可能会遇到多个看似相关的附属统计量。通过将这些统计量提炼为最小附属统计量，他们可以精简分析，使结果和结论的交流变得更加容易。此外，识别最小附属统计量还可以导致更稳健的统计方法。在处理大型数据集或复杂模型时，拥有简化的统计量可以增强计算效率。这在机器学习和数据科学等领域尤为重要，因为算法通常需要在众多参数上进行优化。通过关注最小附属统计量，从业者可以实现更快的收敛和改进的模型性能。此外，最小附属统计量的概念在假设检验中也可以发挥重要作用。在制定原假设和备择假设时，基于最相关的信息做出决策至关重要。利用最小附属统计量可以确保测试建立在最相关的数据基础上，从而提高结果的可靠性。这可以防止由于考虑额外信息而导致的误导性结论。此外，研究最小附属统计量还可以促进对数据基础结构的更深入见解。通过关注仍然捕捉数据集本质的最小方面，统计学家可以揭示在分析全部附属统计量时可能不明显的模式和关系。这可以导致新的发现和各个研究领域的进展。总之，最小附属统计量的概念是统计学领域中的一个重要工具。它使研究人员能够简化分析、增强计算效率、改善假设检验，并深入了解数据。随着统计学家继续完善他们的方法和途径，识别和利用最小附属统计量的重要性不容忽视。接受这一概念无疑将导致未来更有效和更有洞察力的统计实践。