ancillary estimator

简明释义

辅助估计量;

英英释义

例句

1.Researchers often use an ancillary estimator 辅助估计量 to improve the precision of their primary estimates.

研究人员经常使用一个辅助估计量 ancillary estimator来提高他们主要估计的精确度。

2.The ancillary estimator 辅助估计量 was found to be unbiased in the context of this experiment.

在这个实验的背景下，发现辅助估计量 ancillary estimator是无偏的。

3.In statistical analysis, an ancillary estimator 辅助估计量 can provide additional information about the parameters of interest.

在统计分析中，一个辅助估计量 ancillary estimator可以提供关于感兴趣参数的额外信息。

4.By incorporating an ancillary estimator 辅助估计量, the researchers were able to reduce the variance of their estimates significantly.

通过纳入一个辅助估计量 ancillary estimator，研究人员能够显著降低他们估计的方差。

5.An ancillary estimator 辅助估计量 can help in assessing the reliability of the main estimator.

一个辅助估计量 ancillary estimator可以帮助评估主要估计量的可靠性。

作文

In the field of statistics, the concept of an ancillary estimator plays a crucial role in improving the accuracy and efficiency of statistical inference. An ancillary estimator is defined as a statistic that provides additional information about a parameter of interest, but does not depend on the parameter itself. This characteristic makes it distinct from other estimators that are directly related to the parameter being estimated. Understanding the role of ancillary estimators can significantly enhance our ability to make informed decisions based on data analysis.To illustrate the importance of ancillary estimators, consider a scenario where a researcher is trying to estimate the mean height of a population based on a sample. The sample mean is a common estimator for the population mean; however, it may not always provide the most reliable estimate due to variability in the sample. Here, an ancillary estimator could be introduced, such as the sample variance, which, while not directly estimating the mean, provides insight into the dispersion of the data. By incorporating the ancillary estimator into the analysis, the researcher can gain a better understanding of the reliability of the sample mean and make more accurate inferences about the population mean.Another aspect of ancillary estimators is their use in constructing confidence intervals. When estimating a parameter, it is often valuable to provide a range within which we believe the true parameter lies. By utilizing an ancillary estimator, statisticians can enhance the precision of these intervals. For example, if the researcher knows the distribution of the sample data, they can use an ancillary estimator to adjust the width of the confidence interval based on the variability observed in the sample. This adjustment leads to more robust conclusions and reduces the likelihood of making erroneous inferences.Moreover, ancillary estimators can also assist in hypothesis testing. When testing a hypothesis about a population parameter, the presence of an ancillary estimator can help in determining the power of the test. Power refers to the probability of correctly rejecting a false null hypothesis. By integrating ancillary estimators into the testing framework, researchers can improve the sensitivity of their tests, leading to more reliable outcomes.In conclusion, the concept of an ancillary estimator is vital for statisticians and researchers alike. By providing supplementary information that is independent of the parameter being estimated, ancillary estimators enhance the accuracy of point estimates, improve the construction of confidence intervals, and bolster hypothesis testing. As data analysis continues to evolve, a solid understanding of ancillary estimators will be indispensable for anyone looking to derive meaningful insights from statistical data. Emphasizing the significance of ancillary estimators in statistical methodologies will ultimately lead to more informed decision-making and a deeper understanding of the intricacies of data interpretation.

在统计学领域，辅助估计量的概念在提高统计推断的准确性和效率方面起着至关重要的作用。辅助估计量被定义为提供关于感兴趣参数的额外信息的统计量，但不依赖于该参数本身。这一特征使其与其他直接与被估计参数相关的估计量有所不同。理解辅助估计量的作用可以显著增强我们根据数据分析做出明智决策的能力。为了说明辅助估计量的重要性，考虑一个研究者试图根据样本估计一个人群的平均身高的场景。样本均值是估计总体均值的常见估计量；然而，由于样本中的变异性，它可能并不总能提供最可靠的估计。在这里，可以引入一个辅助估计量，例如样本方差，虽然它并不直接估计均值，但提供了对数据离散度的洞察。通过将辅助估计量纳入分析，研究者可以更好地理解样本均值的可靠性，并对总体均值做出更准确的推断。辅助估计量的另一个方面是它们在构建置信区间中的使用。在估计参数时，通常有价值的是提供一个范围，其中我们相信真实参数存在。通过利用辅助估计量，统计学家可以提高这些区间的精确度。例如，如果研究者知道样本数据的分布，他们可以使用辅助估计量根据样本中观察到的变异性来调整置信区间的宽度。这种调整导致更稳健的结论，并减少了做出错误推断的可能性。此外，辅助估计量还可以帮助假设检验。在测试有关总体参数的假设时，辅助估计量的存在可以帮助确定检验的效能。效能指的是正确拒绝虚无假设的概率。通过将辅助估计量整合到检验框架中，研究人员可以提高检验的敏感性，从而得出更可靠的结果。总之，辅助估计量的概念对于统计学家和研究人员来说至关重要。通过提供独立于被估计参数的补充信息，辅助估计量提高了点估计的准确性，改善了置信区间的构造，并增强了假设检验。随着数据分析的不断发展，深入理解辅助估计量将对任何希望从统计数据中提取有意义见解的人至关重要。强调辅助估计量在统计方法中的重要性，最终将导致更明智的决策和对数据解释复杂性的更深刻理解。