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摘要暂缺

非参数回归中的自助法：局部自适应平滑与置信带AI 解读

The operation of the bootstrap in the context of nonparametric regression is considered. Bootstrap samples are taken from estimated residuals to study the distribution of a suitably recentered kernel estimator. The application of this principle to the problem of local adaptive choice of bandwidth and to the construction of confidence bands is investigated and compared with a direct method based on asymptotic means and variances. The technique of the bootstrap is to replace…

摘要暂缺

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…

密度估计平滑参数的另一种交叉验证方法AI 解读

Cross-validation with Kullback-Leibler loss function has been applied to the choice of a smoothing parameter in the kernel method of density estimation. A framework for this problem is constructed and used to derive an alternative method of cross-validation, based on integrated squared error, recently also proposed by Rudemo (1982). Hall (1983) has established the consistency and asymptotic optimality of the new method. For small and moderate sized samples, the performances…

概率与概率密度非参数估计中的交叉验证AI 解读

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…

分类数据核方法的一致性札记AI 解读

Aitchison & Aitken (1976) described a kernel method of estimating the cell probabilities of a multivariate categorical distribution. The criterion for choosing the smoothing parameter is shown to be a cross-validatory choice, as observed by Titterington (1980), and consistency is demonstrated.

分类数据分析中核方法一致性的一个注记AI 解读

Aitchison & Aitken (1976) described a kernel method of estimating the cell probabilities of a multivariate categorical distribution. The criterion for choosing the smoothing parameter is shown to be a cross-validatory choice, as observed by Titterington (1980), and consistency is demonstrated.