新的解释和推断方法用于最小子角回归
New explanations and inference for least angle regression
AI总结：
本文提出了一种新的LAR推断方法，通过分析总体相关性参数的分布特性，提供了一种正式的停止规则和修改后的bootstrap方法，用于解释变量进入和不确定性量化。
摘要：
Efron等人（2004）引入了最小子角回归（LAR）作为一种用于线性预测的算法，旨在作为逐步选择的替代方法，并与惩罚回归有联系。然而，LAR一直保持 somewhat 的
英文摘要：
Efron et al. (2004) introduced least angle regression (LAR) as an algorithm for linear predictions, intended as an alternative to forward selection with connections to penalized regression. However, LAR has remained somewhat of a "black box," where some basic behavioral properties of LAR output are not well understood, including an appropriate termination point for the algorithm. We provide a novel framework for inference with LAR, which also allows LAR to be understood from new perspectives with several newly developed mathematical properties. The LAR algorithm at a data level can viewed as estimating a population counterpart "path" that organizes a response mean along regressor variables which are ordered according to a decreasing series of population "correlation" parameters; such parameters are shown to have meaningful interpretations for explaining variable contributions whereby zero correlations denote unimportant variables. In the output of LAR, estimates of all non-zero population correlations turn out to have independent normal distributions for use in inference, while estimates of zero-valued population correlations have a certain non-normal joint distribution. These properties help to provide a formal rule for stopping the LAR algorithm. While the standard bootstrap for regression can fail for LAR, a modified bootstrap provides a practical and formally justified tool for interpreting the entrance of variables and quantifying uncertainty in estimation. The LAR inference method is studied through simulation and illustrated with data examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
