permissible estimator

简明释义

允许估计量

英英释义

例句

1.The concept of a permissible estimator is crucial in econometrics for deriving consistent estimates.

在计量经济学中，可接受的估计量的概念对于推导一致的估计是至关重要的。

2.Researchers often choose a permissible estimator to ensure the validity of their results.

研究人员通常选择一个可接受的估计量以确保结果的有效性。

3.A permissible estimator can be defined as any estimator that does not violate the assumptions of the model.

一个可接受的估计量可以定义为任何不违反模型假设的估计量。

4.In statistical analysis, a permissible estimator is one that meets certain conditions required for unbiasedness.

在统计分析中，可接受的估计量是指满足无偏性所需的某些条件的估计量。

5.When conducting experiments, it is important to use a permissible estimator to achieve reliable outcomes.

在进行实验时，使用可接受的估计量以获得可靠的结果非常重要。

作文

In the field of statistics, the concept of a permissible estimator is crucial for understanding how we can make inferences about a population based on sample data. An estimator is a rule or formula that provides an estimate of a parameter based on observed data. However, not all estimators are created equal; some may be biased or inefficient, while others may meet certain criteria that make them more acceptable for statistical analysis. This is where the notion of a permissible estimator comes into play.A permissible estimator is defined as an estimator that adheres to specific conditions or constraints imposed by the statistical framework in which it operates. These conditions often relate to bias, variance, and mean squared error (MSE). For instance, an estimator may be considered permissible if it is unbiased, meaning that its expected value equals the true parameter being estimated. This property is vital because it ensures that, on average, the estimator will provide accurate estimates across many samples.In practical applications, researchers often seek to identify permissible estimators that not only maintain unbiasedness but also minimize variance. The trade-off between bias and variance is a fundamental aspect of statistical estimation, known as the bias-variance tradeoff. An estimator that is too complex might fit the sample data very closely but could lead to overfitting, resulting in high variance and poor generalization to new data. Conversely, a simpler estimator may have low variance but could introduce bias, thus failing to capture the underlying patterns in the data accurately.To illustrate the concept further, consider the case of estimating the mean of a population. The sample mean is one of the most commonly used permissible estimators for this purpose. It is calculated by summing all the observed values in a sample and dividing by the number of observations. The sample mean is an unbiased estimator of the population mean, as it tends to converge to the true mean as the sample size increases. Therefore, it satisfies the criteria of being a permissible estimator under the assumption of random sampling from the population.Moreover, the identification of permissible estimators extends beyond just unbiasedness. In many cases, researchers also look for estimators that have desirable properties such as consistency and efficiency. A consistent estimator converges in probability to the true parameter value as the sample size grows, while an efficient estimator has the smallest possible variance among all unbiased estimators. These additional properties help ensure that the estimator performs well under various circumstances, making it a robust choice for statistical inference.In conclusion, the concept of a permissible estimator plays a pivotal role in the realm of statistics. By adhering to specific criteria regarding bias, variance, and overall performance, these estimators facilitate more reliable and valid inferences about populations based on sample data. As statisticians continue to develop new methods and refine existing ones, the quest for identifying and utilizing permissible estimators remains an essential aspect of ensuring the integrity and accuracy of statistical analyses. Understanding this concept is not only vital for academic pursuits but also for practical applications in fields ranging from economics to healthcare, where data-driven decisions are paramount.

在统计学领域，可接受估计量的概念对于理解如何基于样本数据对总体进行推断至关重要。估计量是一个规则或公式，它根据观察到的数据提供参数的估计。然而，并非所有估计量都是平等的；有些可能是有偏的或效率低下的，而另一些可能符合某些条件，使它们在统计分析中更为可接受。这就是可接受估计量概念的来源。可接受估计量被定义为遵循特定条件或约束的估计量，这些条件通常与偏差、方差和均方误差（MSE）有关。例如，如果一个估计量是无偏的，即其期望值等于被估计的真实参数，那么它可能被认为是可接受的。这个属性至关重要，因为它确保了在多次抽样中，估计量平均会提供准确的估计。在实际应用中，研究人员通常寻求识别不仅保持无偏而且最小化方差的可接受估计量。偏差和方差之间的权衡是统计估计的基本方面，被称为偏差-方差权衡。一个过于复杂的估计量可能非常紧密地拟合样本数据，但可能导致过拟合，从而导致高方差和对新数据的较差泛化。相反，一个简单的估计量可能具有低方差，但可能引入偏差，因此未能准确捕捉数据中的潜在模式。为了进一步说明这一概念，考虑估计总体均值的情况。样本均值是用于此目的的最常用的可接受估计量之一。它通过将样本中所有观察值相加并除以观察数量来计算。样本均值是总体均值的无偏估计量，因为随着样本大小的增加，它趋向于收敛到真实均值。因此，在随机抽样的假设下，它满足成为可接受估计量的标准。此外，识别可接受估计量不仅限于无偏性。在许多情况下，研究人员还寻找具有一致性和效率等理想属性的估计量。一致性估计量是指随着样本大小的增长，它的概率逐渐收敛到真实参数值，而有效估计量则在所有无偏估计量中具有最小的方差。这些附加属性有助于确保估计量在各种情况下表现良好，使其成为统计推断的稳健选择。总之，可接受估计量的概念在统计学领域中发挥着关键作用。通过遵循关于偏差、方差和整体性能的特定标准，这些估计量促进了基于样本数据对总体进行更可靠和有效的推断。随着统计学家不断开发新方法和完善现有方法，识别和利用可接受估计量的追求仍然是确保统计分析的完整性和准确性的一个重要方面。理解这一概念不仅对学术研究至关重要，也对经济学、医疗保健等领域的实际应用至关重要，在这些领域中，基于数据的决策至关重要。