heteroscedastic

简明释义

英[ˌhɛt.ə.rəʊ.skiˈdæs.tɪk]美[ˌhɛt.ə.roʊ.skiˈdæs.tɪk]

adj. 异方差的；异质变异性的

英英释义

单词用法

同义词

反义词

例句

1.The model which has such kind of property is referred to as heteroscedastic regression model.

扰动项具有异方差性的模型称为异方差模型。

2.The main contributions are as follows:1. Based on several nonparametric estimation theories, several estimation expressions of conditional heteroscedastic function are constructed.

主要研究结果如下：1。基于几种非参数估计理论，构造了非参数自回归模型条件方差函数的非参数估计表达式。

3.A method for heteroscedastic analysis is presented, which includes the homoscedastic and the heteroscedastic analysis of different means.

提出一种异方差分析方法，包括异均值方差分析和异均值异方差分析。

4.The main contributions are as follows:1. Based on several nonparametric estimation theories, several estimation expressions of conditional heteroscedastic function are constructed.

主要研究结果如下：1。基于几种非参数估计理论，构造了非参数自回归模型条件方差函数的非参数估计表达式。

5.This paper presents a single factor heteroscedastic model, deduce a method of this heteroscedastic analysis, and presents the estimation of mean and variance in this model.

本文提出了一种单因子异方差模型，导出这种异方差分析方法，并给出了模型中均值与方差的估计。

6.A common way to detect heteroscedasticity 异方差性 is by using a residual plot.

检测异方差性 异方差性的常用方法是使用残差图。

7.In regression analysis, we often check for heteroscedasticity 异方差性 to ensure that the variance of errors is constant.

在回归分析中，我们通常检查是否存在异方差性 异方差性，以确保误差的方差是恒定的。

8.If your data exhibits heteroscedasticity 异方差性, you may need to transform your variables.

如果你的数据表现出异方差性 异方差性，你可能需要对变量进行变换。

9.Applying weighted least squares can help address heteroscedasticity 异方差性 in your model.

应用加权最小二乘法可以帮助解决模型中的异方差性 异方差性问题。

10.The presence of heteroscedasticity 异方差性 can lead to inefficient estimates in linear regression.

在线性回归中，存在异方差性 异方差性可能导致估计不够有效。

作文

In the realm of statistics and econometrics, understanding the concept of heteroscedastic is crucial for accurate data analysis and interpretation. The term heteroscedastic refers to a situation in which the variability of a variable is unequal across the range of values of a second variable that predicts it. This phenomenon often arises in regression analysis, where the assumption of constant variance of the error terms is violated. When the errors exhibit heteroscedastic behavior, it can lead to inefficient estimates and affect the validity of hypothesis tests. To illustrate this concept, consider a simple linear regression model where we are trying to predict the income of individuals based on their years of education. If the variance of income increases with more years of education, we are dealing with a heteroscedastic scenario. For instance, individuals with lower educational attainment may have incomes clustered around a certain level, while those with higher education might exhibit a wider range of incomes. This increasing spread of income as education rises demonstrates heteroscedastic behavior.The implications of heteroscedastic data are significant. When conducting regression analysis, if we fail to address heteroscedastic errors, our ordinary least squares (OLS) estimates remain unbiased but are no longer efficient. This inefficiency means that our confidence intervals and hypothesis tests may be misleading, leading to incorrect conclusions about the relationships between variables.To detect heteroscedastic errors, statisticians often use graphical methods such as residual plots, which display the residuals of a regression model against the fitted values. If the plot shows a pattern (for example, a funnel shape), it indicates the presence of heteroscedastic errors. Additionally, formal tests like the Breusch-Pagan test or White test can be employed to statistically assess the presence of heteroscedastic behavior in the data.Once heteroscedastic errors are identified, there are several methods to address this issue. One common approach is to use weighted least squares (WLS) regression, which gives different weights to observations based on their variance. This method aims to stabilize the variance across the range of predictors, thus yielding more reliable estimates. Another approach is to transform the dependent variable, such as applying a logarithmic transformation, which can help mitigate the heteroscedastic nature of the data.In conclusion, the understanding of heteroscedastic behavior is essential for anyone involved in data analysis, particularly in fields such as economics, finance, and social sciences. By recognizing the implications of heteroscedastic errors and employing appropriate methods to address them, researchers can improve the accuracy and reliability of their findings. As data continues to grow in complexity, the ability to identify and manage heteroscedastic conditions will remain a vital skill for statisticians and analysts alike.

在统计学和计量经济学的领域中，理解异方差性的概念对于准确的数据分析和解释至关重要。术语异方差性指的是在第二个变量预测的范围内，一个变量的变异性不均等的情况。这种现象通常出现在回归分析中，其中误差项的常数方差假设被违反。当误差表现出异方差性行为时，它可能导致低效的估计，并影响假设检验的有效性。为了说明这个概念，考虑一个简单的线性回归模型，我们试图根据个人的教育年限预测其收入。如果随着教育年限的增加，收入的方差也增加，那么我们就面临异方差性的场景。例如，受教育程度较低的个人可能收入集中在某个水平，而受教育程度较高的人可能展示出更广泛的收入范围。这种随着教育的提高而增加的收入分散性展示了异方差性行为。异方差性数据的影响是显著的。在进行回归分析时，如果我们未能处理异方差性错误，我们的普通最小二乘（OLS）估计仍然是无偏的，但不再是有效的。这种低效意味着我们的置信区间和假设检验可能会产生误导，从而导致对变量之间关系的错误结论。为了检测异方差性错误，统计学家通常使用图形方法，例如残差图，显示回归模型的残差与拟合值的关系。如果图中显示出某种模式（例如，漏斗形状），则表明存在异方差性错误。此外，Breusch-Pagan检验或White检验等正式检验可以用来统计评估数据中异方差性行为的存在。一旦识别出异方差性错误，就有几种方法可以解决这个问题。一种常见的方法是使用加权最小二乘（WLS）回归，根据观察值的方差给予不同的权重。这种方法旨在稳定预测变量范围内的方差，从而产生更可靠的估计。另一种方法是对因变量进行变换，例如应用对数变换，这可以帮助减轻数据的异方差性特征。总之，理解异方差性行为对于任何参与数据分析的人都是至关重要的，特别是在经济学、金融学和社会科学等领域。通过认识到异方差性错误的影响并采用适当的方法来解决这些问题，研究人员可以提高其发现的准确性和可靠性。随着数据复杂性的不断增长，识别和管理异方差性条件的能力将始终是统计学家和分析师必备的重要技能。