The Little Bootstrap and other Methods for Dimensionality Selection in Regression: X-Fixed Prediction Error
Little Bootstrap 与回归维度选择：固定设计下的预测误差AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要研究一般回归的变量与维度选择，没有宏观预测、金融收益预测或其他所列细分领域的直接证据。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
Little Bootstrap 与回归维度选择：固定设计下的预测误差
- 研究问题
- 在变量筛选生成的一组回归子模型中，如何估计固定解释变量设计上的预测误差，并据此选择模型维度？
- 方法与思路
- 作者提出 little bootstrap，以重用数据估计各子模型的预测误差，再据此选维度，并用解析例子及模拟比较其他方法。
- 材料陈述的贡献
- 摘要称该方法给出近乎无偏的子模型预测误差估计，比较中选择表现较好，并指出 Cp 等方法存在较大的误差估计偏差。
- 阅读关注点
- 应核对固定设计预测误差的定义、变量筛选是否纳入重抽样过程，以及近乎无偏和比较结论依赖的模型与样本条件。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；作者对比较方法的概括不能视为普遍结论，也不能混同固定设计与新设计预测。
原文摘要
When a regression problem contains many predictor variables, it is rarely wise to try to fit the data by means of a least squares regression on all of the predictor variables. Usually, a regression equation based on a few variables will be more accurate and certainly simpler. There are various methods for picking “good” subsets of variables, and programs that do such procedures are part of every widely used statistical package. The most common methods are based on stepwise addition or deletion of variables and on “best subsets.” The latter refers to a search method that, given the number of variables to be in the equation (say, five), locates that regression equation based on five variables that has the lowest residual sum of squares among all five variable equations. All of these procedures generate a sequence of regression equations, the first based on one variable, the next based on two variables, and so on. Each member of this sequence is called a submodel and the number of variables in the equation is the dimensionality of the submodel. A complex problem is determining which submodel of the generated sequence to select. Statistical packages use various ad hoc selection methods, including F to enter, F to delete, Cp , and t-value cutoffs. Our approach to this problem is through the criterion that a good selection procedure selects dimensionality so as to give low prediction error (PE), where the PE of a regression equation is its expected squared error over the points in the X design. Because the true PE is unknown, the use of this criteria must be based on PE estimates. We introduce a method called the little bootstrap, which gives almost unbiased estimates for submodel PEs and then uses these to do submodel selection. Comparison is made to Cp and other methods by analytic examples and simulations. Little bootstrap does well—Cp and, by implication, all selection methods not based on data reuse give highly biased results and poor subset selection.