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矩阵与数组型统计对象的维度折叠AI 解读

We consider dimension reduction for regression or classification in which the predictors are matrix- or array-valued. This type of predictor arises when measurements are obtained for each combination of two or more underlying variables—for example, the voltage measured at different channels and times in electroencephalography data. For these applications, it is desirable to preserve the array structure of the reduced predictor (e.g., time versus channel), but this cannot be…

基于预测的选择准则之最优性与估计量收敛速度AI 解读

Summary Several estimators of squared prediction error have been suggested for use in model and bandwidth selection problems. Among these are cross-validation, generalized cross-validation and a number of related techniques based on the residual sum of squares. For many situations with squared error loss, e.g. nonparametric smoothing, these estimators have been shown to be asymptotically optimal in the sense that in large samples the estimator minimizing the selection…

变量选择问题中的观测影响评估AI 解读

Variable selection techniques are often used in combination with multiple linear regression to produce a parsimonious model that fits the data well. It is clearly undesirable for the final model to depend strongly on the inclusion of a few influential cases in the data set. This article discusses a measure of influence of single cases on the final model, based on a similar measure used in ordinary multiple regression. When variables are selected objectively, deletion of…

变量选择问题中的观测影响评估AI 解读

Variable selection techniques are often used in combination with multiple linear regression to produce a parsimonious model that fits the data well.It is clearly undesirable for the final model to depend strongly on the inclusion of a few influential cases (data points) in the data set.This article discusses a measure of influence of single cases on the final model, based on a similar measure used in ordinary multiple regression.When variables are selected objectively using…