statistical efficiency

简明释义

统计有效性

英英释义

例句

1.The new estimator was found to have higher statistical efficiency than the previous model, which means it provides more accurate results with fewer samples.

新的估计量被发现具有更高的统计效率，这意味着它在使用更少的样本时提供更准确的结果。

2.In clinical trials, achieving statistical efficiency is crucial for minimizing the number of participants while still obtaining reliable data.

在临床试验中，实现统计效率对于在获得可靠数据的同时最小化参与者人数至关重要。

3.Researchers often seek methods that enhance statistical efficiency to improve the quality of their analyses.

研究人员通常寻找提高统计效率的方法，以改善他们分析的质量。

4.The concept of statistical efficiency helps statisticians choose the best methods for data collection.

统计效率的概念帮助统计学家选择最佳的数据收集方法。

5.A well-designed survey can significantly increase statistical efficiency by reducing measurement error.

设计良好的调查可以通过减少测量误差显著提高统计效率。

作文

In the field of statistics, the concept of statistical efficiency plays a crucial role in determining the quality and reliability of estimators. Essentially, statistical efficiency refers to the effectiveness of an estimator in producing accurate and precise estimates with the least amount of variability. An efficient estimator is one that achieves the lowest possible variance among all unbiased estimators for a given parameter. This is particularly important in research and data analysis, where making informed decisions based on statistical results is paramount.To better understand statistical efficiency, it is important to consider the context in which estimators are used. For instance, suppose a researcher is trying to estimate the average height of a population based on a sample. The estimator used must not only be unbiased—meaning that, on average, it hits the true population parameter—but also efficient. If two different estimators yield the same unbiased estimate, the one with the smaller variance is considered more efficient. This efficiency ensures that the conclusions drawn from the data are more reliable and robust.One of the most common measures of statistical efficiency is the Cramér-Rao Lower Bound (CRLB), which provides a theoretical lower limit for the variance of unbiased estimators. According to this principle, if an estimator reaches the CRLB, it is deemed efficient. Researchers often strive to develop estimators that not only meet the unbiased criterion but also achieve this lower bound, thereby maximizing their statistical efficiency.Moreover, the implications of statistical efficiency extend beyond just theoretical statistics; they have practical applications in various fields, including economics, medicine, and social sciences. For instance, in clinical trials, researchers aim to design studies that maximize statistical efficiency to ensure that the results are both valid and applicable to the larger population. By using efficient sampling methods and appropriate statistical models, they can minimize the required sample size while still obtaining reliable estimates of treatment effects.In conclusion, statistical efficiency is a fundamental concept in statistics that influences how researchers analyze data and draw conclusions. It emphasizes the importance of using estimators that provide the most accurate results with the least amount of variability. Understanding and applying the principles of statistical efficiency allows statisticians and researchers to make more informed decisions and contribute valuable insights across various disciplines. As the field of statistics continues to evolve, the pursuit of greater statistical efficiency remains a key objective, enhancing the credibility and applicability of statistical findings in real-world scenarios.

在统计学领域，统计效率的概念在确定估计量的质量和可靠性方面起着至关重要的作用。基本上，统计效率指的是估计量在以最小的变异性产生准确而精确的估计方面的有效性。一个高效的估计量是指在给定参数的所有无偏估计量中，方差最低的估计量。这在研究和数据分析中尤为重要，因为基于统计结果做出明智的决策至关重要。为了更好地理解统计效率，重要的是要考虑使用估计量的背景。例如，假设一个研究者试图根据一个样本估计一个人群的平均身高。所使用的估计量不仅必须是无偏的——意味着它在平均情况下命中真实的人口参数——而且还必须是高效的。如果两个不同的估计量产生相同的无偏估计，则方差较小的那个被认为更高效。这种效率确保了从数据中得出的结论更加可靠和稳健。统计效率最常用的衡量标准之一是Cramér-Rao下界（CRLB），它为无偏估计量的方差提供了理论上的下限。根据这一原则，如果一个估计量达到了CRLB，它就被认为是高效的。研究人员通常努力开发不仅满足无偏标准而且达到这一下限的估计量，从而最大化它们的统计效率。此外，统计效率的影响超越了理论统计学；它在经济学、医学和社会科学等各个领域都有实际应用。例如，在临床试验中，研究人员旨在设计最大化统计效率的研究，以确保结果既有效又适用于更大的人群。通过使用高效的抽样方法和适当的统计模型，他们可以在仍然获得可靠的治疗效果估计的同时，最小化所需的样本量。总之，统计效率是统计学中的一个基本概念，它影响着研究人员如何分析数据和得出结论。它强调使用能够以最小的变异性提供最准确结果的估计量的重要性。理解和应用统计效率的原则使统计学家和研究人员能够做出更明智的决策，并在各个学科中贡献有价值的见解。随着统计学领域的不断发展，追求更高的统计效率仍然是一个关键目标，增强了统计发现的可信度和适用性。