对离散分布的线性有条件预期
Thaddeus Tarpey1, Richard D Sanders2
1Department of Mathematics and Statistics, Wright State University, Dayton, OH, USA.
Journal of applied statistics
|October 7, 2024
概括
离散的多变量分布经常表现出线性条件期望,这一发现得到了模拟的支持. 这项研究澄清了连续和离散数据分析的统计假设.
科学领域:
- 统计 统计 统计 统计
- 可能性理论概率理论.
- 计量经济学 计量经济学
背景情况:
- 许多连续数据的统计模型假定线性条件期望.
- 多变量数据组件经常使用离散的顺序尺度来测量,这些尺度来自底层的连续潜变量.
- 了解这些离散分布的属性对于准确的统计推理至关重要.
研究的目的:
- 调查常见的离散多变量分布是否保持线性有条件预期.
- 为这些分布的行为提供理论结果和经验证据.
- 根据统计方法对混合连续和离散组件的数据的应用提供信息.
主要方法:
- 对于离散的双变量和三变量分布的理论性质的导出.
- 进行模拟研究以经验验证发现.
- 在离谱化下分析条件期望.
主要成果:
- 离散的二变和三变分布的常见例子表明了线性有条件的预期.
- 理论结果得到模拟结果的支持.
- 这些发现适用于潜在连续变量的典型离散方法.
结论:
- 线性条件期望的假设通常保留在常见的离散多变量分布中.
- 这项研究验证了在某些离散数据环境中假定线性条件期望的方法的使用.
- 为使用顺序或离散数据进行更强大的统计建模提供了基础.
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