best estimator; preferred estimator

简明释义

最佳估计量

英英释义

例句

1.When building predictive models, data scientists often look for a preferred estimator 优选估计量 that minimizes bias.

在构建预测模型时，数据科学家通常寻找一个 优选估计量 preferred estimator，以最小化偏差。

2.For linear regression, the ordinary least squares method provides the best estimator 最佳估计量 of the coefficients.

对于线性回归，普通最小二乘法提供了系数的 最佳估计量 best estimator。

3.In statistical analysis, the best estimator 最佳估计量 for the mean is often the sample mean.

在统计分析中，最佳估计量 best estimator 通常是样本均值。

4.In machine learning, the choice of a preferred estimator 优选估计量 can significantly impact the model's performance.

在机器学习中，选择一个 优选估计量 preferred estimator 会显著影响模型的性能。

5.The best estimator 最佳估计量 for the variance can be calculated using the unbiased sample variance formula.

方差的 最佳估计量 best estimator 可以使用无偏样本方差公式计算。

作文

In the realm of statistics and data analysis, the terms best estimator and preferred estimator play a crucial role in determining how we interpret and utilize data. An estimator is a rule or a method for estimating an unknown quantity based on observed data. The distinction between a best estimator and a preferred estimator often hinges on specific criteria that one might prioritize during analysis.A best estimator is typically defined as the one that minimizes the mean squared error (MSE) or provides the most accurate predictions when compared to other estimators. This concept is grounded in the theory of estimation, where different estimators are evaluated based on their bias and variance. An estimator with low bias and low variance is generally considered the best because it provides reliable and consistent estimates across various samples.On the other hand, a preferred estimator may not necessarily be the one that minimizes MSE. Instead, it reflects the analyst's priorities and the context of the data. For example, in some scenarios, an estimator that introduces a small amount of bias might be preferred if it significantly reduces variance, leading to more stable estimates. This choice often depends on the specific goals of the analysis and the nature of the data being examined.To illustrate this further, consider a scenario in which a researcher is trying to estimate the average height of a population. They may have two estimators available: one that is unbiased but has a high variance, and another that is biased but has lower variance. If the researcher prioritizes precision over accuracy, they might choose the biased estimator as their preferred estimator, even though it is not the best estimator in terms of MSE.Furthermore, the choice between a best estimator and a preferred estimator can also be influenced by external factors such as computational efficiency, ease of interpretation, and the availability of data. In practical applications, analysts often face trade-offs that require them to weigh the benefits of accuracy against the practicalities of implementation. Therefore, understanding these concepts is essential for making informed decisions in statistical modeling and estimation.In conclusion, the terms best estimator and preferred estimator encapsulate important considerations in statistical analysis. While the best estimator aims for the most accurate predictions, the preferred estimator reflects the analyst's context-specific choices. Recognizing the nuances between these estimators allows researchers and practitioners to approach data analysis with a more comprehensive understanding, ultimately leading to better decision-making and insights from their data. As we continue to navigate the complexities of data analysis, keeping these definitions in mind will enhance our ability to choose the right methods for our specific needs and objectives.

在统计学和数据分析领域，术语最佳估计量和优选估计量在确定我们如何解释和利用数据方面起着至关重要的作用。估计量是基于观察数据来估计未知数量的规则或方法。最佳估计量和优选估计量之间的区别通常取决于在分析过程中可能优先考虑的特定标准。最佳估计量通常被定义为最小化均方误差（MSE）或与其他估计量相比提供最准确预测的估计量。这个概念基于估计理论，在该理论中，不同的估计量根据其偏差和方差进行评估。具有低偏差和低方差的估计量通常被认为是最佳的，因为它提供了在各种样本中可靠且一致的估计。另一方面，优选估计量可能并不一定是最小化均方误差的估计量。相反，它反映了分析师的优先事项和数据的上下文。例如，在某些情况下，如果一个引入少量偏差的估计量显著降低方差，从而导致更稳定的估计，则可能会优先选择该估计量。这个选择往往取决于分析的具体目标和所检查数据的性质。为了进一步说明这一点，考虑一个研究人员试图估计一个人群的平均身高的场景。他们可能有两个可用的估计量：一个是无偏的，但方差较高，另一个是有偏的，但方差较低。如果研究人员优先考虑精度而非准确性，他们可能会选择有偏的估计量作为他们的优选估计量，尽管它在均方误差方面不是最佳估计量。此外，选择最佳估计量和优选估计量也可能受到外部因素的影响，例如计算效率、易于解释性和数据的可用性。在实际应用中，分析师经常面临权衡，需要权衡准确性的好处与实施的实用性。因此，理解这些概念对于在统计建模和估计中做出明智的决策至关重要。总之，最佳估计量和优选估计量这两个术语概括了统计分析中的重要考虑因素。虽然最佳估计量旨在实现最准确的预测，但优选估计量反映了分析师的上下文特定选择。认识到这些估计量之间的细微差别使研究人员和从业人员能够以更全面的理解来接近数据分析，最终导致更好的决策和对数据的洞察。随着我们继续应对数据分析的复杂性，牢记这些定义将增强我们选择适合我们特定需求和目标的方法的能力。