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相关概念视频

Variance01:15

Variance

9.3K
 The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.
The standard deviation measures the spread in the same units as the...
9.3K
Estimating Population Mean with Known Standard Deviation01:16

Estimating Population Mean with Known Standard Deviation

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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
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Estimating Population Mean with Unknown Standard Deviation01:22

Estimating Population Mean with Unknown Standard Deviation

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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the...
7.6K
Correlation and Regression00:53

Correlation and Regression

1.2K
In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a...
1.2K
Empirical Method to Interpret Standard Deviation01:09

Empirical Method to Interpret Standard Deviation

5.1K
The empirical rule, also known as the three-sigma rule, allows a statistician to interpret the standard deviation in a normally distributed dataset. The rule states that 68% of the data lies within one standard deviation from the mean, 95% lies within two standard deviations from the mean, and 99.7% lies within three standard deviations from the mean. Additionally, this rule is also called the 68-95-99.7 rule.
This rule is used widely in statistics to calculate the proportion of data values...
5.1K
Variation01:19

Variation

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An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation, which is the square root of variance.
When independent and dependent variables are plotted on a scatter plot, the slope of a line is a value that describes the rate of change between the two...
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相关实验视频

Updated: Jun 5, 2025

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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关于平均差异相关性模型的GEE:差异估计和模型选择.

Zhenyu Xu1, Jason P Fine2, Wenling Song3

  • 1Department of Statistics, University of Connecticut, Storrs, Connecticut.

Statistics in medicine
|December 12, 2024
PubMed
概括
此摘要是机器生成的。

对集群数据的概括估计方程 (GEE) 分析得到了一种新方法的改进,该方法正确估计差异和相关性. 这种方法增强了对平均值,方差和相关性结构的模型选择.

关键词:
一般化估计方程的估计方程.模型选择标准模型选择标准这是一个三明治估计器.工作协差结构的工作协差结构.

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科学领域:

  • 统计 统计 统计 统计
  • 生物统计学 生物统计学
  • 计量经济学 计量经济学

背景情况:

  • 一般化估计方程 (GEE) 对于分析集群数据而不是假设完全的多变量分布至关重要.
  • 最近的方法,比如罗和潘的方法,共同模拟平均值,方差和相关性.
  • 这些模型是Yan和Fine更一般的估计方程的具体情况.

研究的目的:

  • 为了解决罗和潘对集群数据的方差和相关性估计的局限性.
  • 引入一种新的模型选择标准,用于同时选择平均尺度-相关性模型.
  • 扩展 geepack R 包,以提高协差矩阵的灵活性.

主要方法:

  • 描述罗和潘的差异估计器面临挑战的模型设置.
  • 展示了Yan和Fine的估计器如何正确处理嵌套依赖关系.
  • 开发和应用一个新的模型选择标准.
  • 使用三明治差异估计器和模拟研究.

主要成果:

  • 确定了Luo和Pan的差异估计方法有限的特定场景.
  • 证明了Yan和Fine的估计器在计算依赖性的有效性.
  • 通过模拟和真实数据验证了拟议的模型选择标准.
  • 扩展了 geepack,为协差矩阵工作提供了新的选项.

结论:

  • 拟议的方法为集群数据分析提供了改进的差异估计和模型选择.
  • 增强的geepack包为分析复杂的相关数据结构提供了更大的灵活性.
  • 这项工作推进了统计建模中概括估计方程的应用.