asymptotic relative efficiency

简明释义

逼近相对效率;

英英释义

例句

1.The asymptotic relative efficiency 渐近相对效率 of the new estimator was found to be significantly higher than that of the traditional method.

新的估计量的渐近相对效率 渐近相对效率 被发现显著高于传统方法。

2.When analyzing variance, understanding the asymptotic relative efficiency 渐近相对效率 can lead to better model selection.

在分析方差时，理解渐近相对效率 渐近相对效率 可以帮助更好地选择模型。

3.The study revealed that the asymptotic relative efficiency 渐近相对效率 of the new algorithm approaches that of the optimal solution.

研究表明，新算法的渐近相对效率 渐近相对效率 接近最优解的效率。

4.Researchers often compare the asymptotic relative efficiency 渐近相对效率 of different statistical tests to determine which is more effective.

研究人员经常比较不同统计检验的渐近相对效率 渐近相对效率 以确定哪种方法更有效。

5.In large samples, the asymptotic relative efficiency 渐近相对效率 provides a useful measure for evaluating estimators.

在大样本中，渐近相对效率 渐近相对效率 提供了评估估计量的有用指标。

作文

In the realm of statistics and estimation theory, the concept of asymptotic relative efficiency plays a crucial role in comparing the performance of different estimators. It is defined as the ratio of the variances of two estimators as the sample size approaches infinity. This metric allows statisticians to evaluate how well an estimator performs relative to another, particularly in large samples. Understanding asymptotic relative efficiency is essential for researchers who aim to choose the most effective method for estimating parameters in their models.To illustrate this concept, consider two different estimators: one could be the maximum likelihood estimator (MLE) and the other a method of moments estimator (MME). As the sample size increases, the variance of these estimators tends to decrease, which makes them more reliable. The asymptotic relative efficiency helps quantify the efficiency of these estimators by comparing their variances at large sample sizes.For instance, if the MLE has a variance that is half that of the MME as the sample size becomes very large, we can conclude that the MLE is more efficient than the MME. Specifically, we would say that the asymptotic relative efficiency of the MLE relative to the MME is 2. This means that, asymptotically, the MLE requires a smaller sample size to achieve the same level of precision as the MME.The importance of asymptotic relative efficiency extends beyond mere comparison of estimators; it also informs decisions in experimental design and data collection. When researchers are aware of which estimators are more efficient, they can allocate their resources more effectively. For example, if an estimator has a higher asymptotic relative efficiency, it may be preferable to use it, especially when dealing with limited data or when seeking to minimize costs associated with data collection.Moreover, the concept of asymptotic relative efficiency is not only applicable in theoretical statistics but also in practical applications across various fields such as economics, biology, and engineering. In these disciplines, the choice of estimator can significantly affect the conclusions drawn from data analysis. Hence, understanding the relative efficiency of different methods can lead to more accurate models and better decision-making processes.In summary, asymptotic relative efficiency serves as a vital tool in the statistician’s toolkit, providing insights into the comparative effectiveness of different estimators as sample sizes grow. By enabling researchers to identify the most efficient methods, it ultimately contributes to the integrity and reliability of statistical analyses. As the field of statistics continues to evolve, the relevance of asymptotic relative efficiency will remain significant, guiding practitioners in their quest for optimal estimation techniques and enhancing the overall quality of research outcomes.

在统计学和估计理论领域，渐近相对效率的概念在比较不同估计器的表现中起着至关重要的作用。它被定义为当样本大小趋近于无穷大时两个估计器方差的比率。这个指标使统计学家能够评估一个估计器相对于另一个的表现，特别是在大样本中。理解渐近相对效率对于那些希望选择最有效的参数估计方法的研究人员至关重要。为了说明这个概念，可以考虑两种不同的估计器：一种可以是最大似然估计器（MLE），另一种是矩估计器（MME）。随着样本大小的增加，这些估计器的方差往往会减少，使它们更可靠。渐近相对效率通过比较这些估计器在大样本大小下的方差来量化它们的效率。例如，如果MLE的方差在样本大小非常大时是MME的一半，我们可以得出结论，MLE比MME更有效。具体来说，我们可以说MLE相对于MME的渐近相对效率是2。这意味着，从渐近角度看，MLE需要更小的样本量来达到与MME相同的精度水平。渐近相对效率的重要性不仅限于估计器的比较；它还为实验设计和数据收集中的决策提供了信息。当研究人员了解哪些估计器更有效时，他们可以更有效地分配资源。例如，如果某个估计器具有更高的渐近相对效率，那么使用它可能更可取，尤其是在处理有限数据或寻求最小化与数据收集相关的成本时。此外，渐近相对效率的概念不仅适用于理论统计学，还适用于经济学、生物学和工程等各个领域的实际应用。在这些学科中，估计器的选择可能会显著影响从数据分析中得出的结论。因此，理解不同方法的相对效率可以导致更准确的模型和更好的决策过程。总之，渐近相对效率作为统计学家的重要工具，为我们提供了关于不同估计器在样本大小增长时的比较有效性的见解。通过使研究人员能够识别出最有效的方法，它最终有助于统计分析的完整性和可靠性。随着统计学领域的不断发展，渐近相对效率的相关性将继续显著，指导从业者追求最佳估计技术，并提升研究结果的整体质量。