Assessing the Accuracy of Normal Approximations
正态近似准确性的评估AI 解读 ↓
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正态近似准确性的评估
- 研究问题
- 如何以可操作的方式评估正态近似的准确性，尤其是近似似然区域与预测概率区域相对于精确对象的偏差？
- 方法与思路
- 作者提出两种比较方法：比较精确与近似似然的等值曲线，以及比较精确密度与正态近似的选定线积分。
- 材料陈述的贡献
- 摘要称方法能够评估区域包含关系及实际概率含量，并通过牙齿测量的预测分布示例展示近似区域的概率偏差。
- 阅读关注点
- 应核对等值曲线与线积分的选择、精确对象的计算方式，以及与收敛速度和曲率方法比较时采用的准确性标准。
- 阅读边界
- 仅据版本未注明的OpenAlex索引摘要，示例中的概率偏差不能代表一般误差界；计算成本与适用条件未充分说明。
原文摘要
The widespread applicability and use of normal approximations creates a need for methods for assessing their accuracy in an operational fashion. In this article, two new methods are proposed and exemplified. These new methods are based on a comparison of the level curves of an exact likelihood with the level curves of the usual normal approximation to it and on a comparison of selected line integrals of an exact density and a normal approximation to it. The operational usefulness of these methods is compared with the operational usefulness of two well-known existing approaches to assessing the accuracy of approximations, namely convergence rates and the curvature methods of Bates and Watts (1980). As an example, the second method is applied to the Lee—Geisser (1972, 1975) approximation to the predictive distribution of dental measurements on girls at the ages of 8, 10, 12, and 14 years. In this application, the method shows that the 50% central (predictive) probability region has actual (predictive) probability content between 3% and 6% higher, that the approximate 80% central region has actual probability content between 1.7% lower and 4.4% higher, and that the approximate 95% central region has actual probability content between 3.7% lower and 5.6% higher. The first method gives the smallest approximate likelihood region that contains the exact likelihood region and the largest approximate likelihood region contained in the exact region.