inefficient estimator

简明释义

无效估计量

英英释义

例句

1.When dealing with small sample sizes, relying on an inefficient estimator can significantly skew results.

在处理小样本时，依赖于一个低效估计量可能会显著扭曲结果。

2.In statistical analysis, using the sample mean as an inefficient estimator of the population mean can lead to larger variances in our predictions.

在统计分析中，使用样本均值作为总体均值的低效估计量可能导致我们预测的方差更大。

3.An inefficient estimator can result in higher costs when making decisions based on its output.

基于其输出做出决策时，低效估计量可能导致更高的成本。

4.The team decided to abandon the inefficient estimator after realizing it was not providing reliable results.

团队在意识到该低效估计量未能提供可靠结果后决定放弃它。

5.The researcher found that the maximum likelihood estimator was more efficient than the inefficient estimator they initially used.

研究人员发现，最大似然估计量比他们最初使用的低效估计量更有效。

作文

In the realm of statistics, we often encounter various methods for estimating parameters from sample data. One such method involves the use of estimators, which are rules or formulas that provide estimates of population parameters based on sample statistics. However, not all estimators are created equal. Some are more effective than others in terms of their statistical properties. An important concept in this discussion is that of an inefficient estimator, which refers to an estimator that does not achieve the lowest possible variance among all unbiased estimators. In simpler terms, it means that the estimator is less precise compared to other available estimators.To understand why an inefficient estimator is a critical concept, it is essential to grasp the importance of efficiency in statistical estimation. Efficiency measures how well an estimator uses the information contained in the sample data. An efficient estimator provides estimates that are close to the true parameter value with minimal variability. This is particularly crucial in fields such as economics, medicine, and social sciences, where accurate parameter estimation can lead to better decision-making and policy formulation.For example, consider a scenario where a researcher is trying to estimate the average height of adult males in a city. If the researcher uses a simple random sample but employs an inefficient estimator to calculate the mean height, the resulting estimate may have a larger margin of error than necessary. This inefficiency could arise from various factors, including a small sample size or using a biased sampling method. Consequently, the researcher may draw incorrect conclusions about the population, leading to flawed recommendations.On the other hand, using an efficient estimator in this scenario would yield a more reliable estimate of the average height. Efficient estimators typically have desirable properties such as consistency and asymptotic normality, which means that as the sample size increases, the estimates converge to the true parameter value. This reliability is vital for researchers and practitioners who depend on accurate data analysis to inform their work.Moreover, it is worth noting that the concept of an inefficient estimator is not limited to a single context; it can apply to various statistical models and estimation techniques. For instance, in linear regression, if a researcher uses a method that does not minimize the sum of squared residuals effectively, they may end up with an inefficient estimator for the regression coefficients. This inefficiency can lead to biased predictions and poor model performance.In conclusion, understanding the implications of using an inefficient estimator is vital for anyone involved in statistical data analysis. It highlights the importance of choosing appropriate estimation techniques to ensure that the results are both accurate and reliable. By being aware of the potential pitfalls associated with inefficient estimators, researchers can make informed decisions that enhance the quality of their work. Ultimately, striving for efficiency in statistical estimation is not just a theoretical exercise; it has real-world consequences that can significantly impact research outcomes and practical applications across various fields.

在统计学领域，我们经常会遇到各种方法来从样本数据中估计参数。其中一种方法涉及使用估计量，它是提供基于样本统计量的总体参数估计的规则或公式。然而，并非所有的估计量都是平等的。有些在统计特性方面比其他估计量更有效。在这个讨论中，一个重要的概念是低效估计量，它指的是一个没有在所有无偏估计量中达到最低方差的估计量。简单来说，这意味着该估计量的精确度低于其他可用的估计量。要理解为什么低效估计量是一个关键概念，必须掌握效率在统计估计中的重要性。效率衡量的是估计量如何利用样本数据中包含的信息。有效的估计量提供的估计值与真实参数值接近，并且变异性最小。这在经济学、医学和社会科学等领域尤为重要，因为准确的参数估计可以导致更好的决策和政策制定。例如，考虑一个研究者试图估计一个城市成年男性的平均身高的场景。如果研究者使用简单随机样本，但采用低效估计量来计算平均身高，那么最终的估计可能具有比必要的更大的误差范围。这种低效可能源于各种因素，包括样本量小或使用了偏见的抽样方法。因此，研究者可能会对总体得出错误的结论，从而导致有缺陷的建议。另一方面，在这种情况下使用有效的估计量将产生更可靠的平均身高估计。有效的估计量通常具有一致性和渐进正态性等理想特性，这意味着随着样本量的增加，估计值会收敛到真实参数值。这种可靠性对于依赖准确数据分析来指导工作的研究人员和从业者至关重要。此外，值得注意的是，低效估计量的概念并不限于单一背景；它可以适用于各种统计模型和估计技术。例如，在线性回归中，如果研究者使用一种未能有效最小化残差平方和的方法，他们可能最终会得到回归系数的低效估计量。这种低效可能导致偏差的预测和糟糕的模型性能。总之，了解使用低效估计量的影响对于任何参与统计数据分析的人来说都是至关重要的。它突出了选择适当估计技术以确保结果既准确又可靠的重要性。通过意识到与低效估计量相关的潜在陷阱，研究人员可以做出明智的决策，从而提高其工作的质量。最终，在统计估计中追求效率不仅仅是一个理论上的练习；它具有现实世界的后果，可能会显著影响各个领域的研究结果和实际应用。