asymptotic distribution

简明释义

渐近分布;

英英释义

例句

1.The asymptotic distribution 渐近分布 of the maximum likelihood estimator can be used to construct confidence intervals.

最大似然估计量的渐近分布 渐近分布可以用于构建置信区间。

2.The asymptotic distribution 渐近分布 of estimators can be derived using the method of moments.

估计量的渐近分布 渐近分布可以通过矩法推导得出。

3.In large sample theory, the Central Limit Theorem states that the sample mean will have an asymptotic distribution 渐近分布 that approaches a normal distribution.

在大样本理论中，中心极限定理表明样本均值将具有一种渐近分布 渐近分布，接近正态分布。

4.In Bayesian statistics, the posterior distribution may have an asymptotic distribution 渐近分布 that is normal under certain conditions.

在贝叶斯统计中，后验分布在某些条件下可能具有正态的渐近分布 渐近分布。

5.When analyzing the performance of algorithms, researchers often look at the asymptotic distribution 渐近分布 of their runtime to understand scalability.

在分析算法性能时，研究人员通常关注其运行时间的渐近分布 渐近分布以理解可扩展性。

作文

In the field of statistics and probability theory, the concept of asymptotic distribution is crucial for understanding the behavior of estimators as the sample size approaches infinity. The asymptotic distribution refers to the probability distribution that an estimator converges to as the sample size increases. This concept is particularly important when dealing with large samples, where exact distributions may be difficult to derive or compute. For instance, in many statistical applications, we often rely on the Central Limit Theorem (CLT), which states that the sum (or average) of a large number of independent and identically distributed random variables will tend toward a normal distribution, regardless of the original distribution of the variables. This result highlights the significance of the asymptotic distribution, as it allows statisticians to make inferences about population parameters using sample data.Understanding the asymptotic distribution becomes even more relevant when considering the efficiency of different estimators. For example, the Maximum Likelihood Estimator (MLE) is known to have desirable asymptotic distribution properties, such as being asymptotically unbiased and achieving the Cramér-Rao lower bound in large samples. This means that as the sample size grows, the MLE approaches the true parameter value more closely than other estimators. Therefore, researchers often prefer MLEs due to their favorable asymptotic distribution characteristics.Moreover, the asymptotic distribution plays a vital role in hypothesis testing. When performing tests based on sample data, we often need to determine the critical values or p-values associated with test statistics. As the sample size increases, the distribution of these test statistics can often be approximated by their asymptotic distribution. For example, in large-sample hypothesis testing, it is common to use the normal distribution as an approximation for the test statistic, even if the underlying population distribution is not normal. This reliance on the asymptotic distribution enables researchers to conduct tests and make decisions based on large samples effectively.In practical applications, the concept of asymptotic distribution also extends to various fields, including economics, finance, and machine learning. In econometrics, for instance, researchers often apply regression models to analyze economic data. As the number of observations increases, the estimators derived from these models exhibit asymptotic distribution properties that facilitate inference about economic relationships. Similarly, in finance, portfolio theory relies on asymptotic distribution principles to assess risk and return, helping investors make informed decisions.In conclusion, the notion of asymptotic distribution is a fundamental concept in statistics that provides insight into the behavior of estimators and test statistics as sample sizes grow. It allows statisticians to make valid inferences and decisions based on large sample data, enhancing the reliability of statistical analyses. By understanding the implications of asymptotic distribution, researchers can better navigate the complexities of statistical modeling and hypothesis testing, ultimately leading to more robust conclusions in their respective fields.

在统计学和概率论领域，渐近分布的概念对于理解估计量在样本大小趋近于无穷大时的行为至关重要。渐近分布是指估计量随着样本大小增加而收敛到的概率分布。当处理大样本时，这个概念尤其重要，因为确切的分布可能难以推导或计算。例如，在许多统计应用中，我们通常依赖中心极限定理（CLT），该定理指出，大量独立同分布随机变量的和（或平均值）将趋向于正态分布，无论这些变量的原始分布如何。这一结果突显了渐近分布的重要性，因为它使统计学家能够使用样本数据对总体参数进行推断。理解渐近分布在考虑不同估计量的有效性时变得更加相关。例如，最大似然估计量（MLE）被认为具有良好的渐近分布特性，如在大样本中是渐近无偏的，并且达到了Cramér-Rao下界。这意味着随着样本大小的增长，MLE比其他估计量更接近真实参数值。因此，研究人员通常更喜欢MLE，因为它具有有利的渐近分布特性。此外，渐近分布在假设检验中也发挥着重要作用。在基于样本数据进行检验时，我们通常需要确定与检验统计量相关的临界值或p值。随着样本大小的增加，这些检验统计量的分布通常可以通过它们的渐近分布进行近似。例如，在大样本假设检验中，通常使用正态分布作为检验统计量的近似，即使基础总体分布不是正态的。这种对渐近分布的依赖使研究人员能够有效地进行检验并做出决策。在实际应用中，渐近分布的概念还扩展到多个领域，包括经济学、金融学和机器学习。例如，在计量经济学中，研究人员通常应用回归模型来分析经济数据。随着观察数量的增加，从这些模型中得出的估计量表现出有助于推断经济关系的渐近分布特性。同样，在金融学中，投资组合理论依赖于渐近分布原则来评估风险和回报，帮助投资者做出明智的决策。总之，渐近分布的概念是统计学中的一个基本概念，它提供了关于估计量和检验统计量在样本大小增加时行为的洞察。它使统计学家能够根据大样本数据进行有效的推断和决策，从而增强了统计分析的可靠性。通过理解渐近分布的含义，研究人员可以更好地驾驭统计建模和假设检验的复杂性，最终在各自领域得出更为稳健的结论。