Cross-validation in nonparametric estimation of probabilities and probability densities
Cross-validation in nonparametric estimation of probabilities and probability densities
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DOI：
10.1093/biomet/71.2.341
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发表时间：
1984-08
期刊：
影响因子：
2.7
通讯作者：
A. Bowman;P. Hall;D. Titterington
中科院分区：
文献类型：
--
作者：
A. Bowman;P. Hall;D. Titterington
总结 我们从完全通用的损失度量开始，研究了用于估计单元概率的交叉验证的大样本特性。导出损失函数的必要和充分条件，以使所得估计量保持一致或最小化预期损失。这些结果表明交叉验证对损失函数的形状极其敏感。然而，当损失函数选择正确时，交叉验证可以在大样本中表现良好。我们提供了一种生成具有最佳属性的损失函数的简单方法。在启发式层面上讨论了单变量概率密度函数估计的扩展。
SUMMARY We examine large-sample properties of cross-validation for estimating cell probabilities, starting from a completely general measure of loss. Necessary and sufficient conditions on the loss function are derived for the resulting estimator to be consistent, or to minimize expected loss. These results reveal that cross-validation is extremely sensitive to the shape of the loss function. Nevertheless, when the loss function is chosen correctly, cross-validation can be relied on to perform well for large samples. We provide a simple method of generating loss functions with optimal properties. Extension to the estimation of univariate probability density functions is discussed at a heuristic level.