Convergence of estimative density: criterion for model complexity and sample size
Convergence of estimative density: criterion for model complexity and sample size
复制标题
估计密度的收敛：模型复杂性和样本量的标准
DOI：
10.1007/s00362-022-01309-9
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发表时间：
2023
影响因子：
1.3
通讯作者：
Yo Sheena
中科院分区：
文献类型：
--
作者：
青柳 力;藤原 洋志;山本 博章;Yo Sheena
对于分布的参数模型，考虑模型中最接近模型外真实分布的分布。用Kullback-Leibler散度测量两个分布之间的接近度，最接近的分布称为“信息投影”。最大似然估计量的估计风险定义为信息投影与最大似然估计密度（插入最大似然估计量的预测分布）之间的Kullback-Leibler散度的期望。在此，导出了风险在样本量上的渐近展开式直至二阶，并研究了预测分布与信息投影之间的贝叶斯误差率小于规定值的风险的充分条件。结合这些结果，提出了“p/ncriterion”，用于确定给定模型和样本的估计密度是否足够接近信息投影。这个准则可以构成样本大小或模型选择问题的解决方案。在两个实际数据集上演示了p/ncriteria的使用。
For a parametric model of distributions, the closest distribution in the model to the true distribution located outside the model is considered. Measuring the closeness between two distributions with the Kullback–Leibler divergence, the closest distribution is called the “information projection.” The estimation risk of the maximum likelihood estimator is defined as the expectation of Kullback–Leibler divergence between the information projection and the maximum likelihood estimative density (the predictive distribution with the plugged-in maximum likelihood estimator). Here, the asymptotic expansion of the risk is derived up to the second order in the sample size, and the sufficient condition on the risk for the Bayes error rate between the predictive distribution and the information projection to be lower than a specified value is investigated. Combining these results, the “p/ncriterion” is proposed, which determines whether the estimative density is sufficiently close to the information projection for the given model and sample. This criterion can constitute a solution to the sample size or model selection problem. The use of thep/ncriteria is demonstrated for two practical datasets.
影响因子：
32.8
作者：
Wainwright, Martin J.;Jordan, Michael I.
通讯作者：
Jordan, Michael I.
指数族信息投影的 MLE 收敛速度：模型维数和样本量的判据——完整证明版本——
DOI：
--
发表时间：
2021
期刊：
--
影响因子：
--
作者：
Y. Sheena
通讯作者：
Y. Sheena