Abstract In this article, a linear model with grouped explanatory variables is considered. The idea is to perform an automatic detection of different successive groups of the unknown coefficients under the assumption that the number of groups is of the same order as the sample size. The standard least squares loss function and the quantile loss function are both used together with the fused and adaptive fused penalty to simultaneously estimate and group the unknown parameters. The proper convergence rate is given for the obtained estimators and the upper bound for the number of different successive group is derived. A simulation study is used to compare the empirical performance of the proposed fused and adaptive fused estimators, and a real application on the air quality data demonstrates the practical applicability of the proposed methods.

中文翻译：

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在变量组数量不同的模型中检测相似的连续组

摘要 在本文中，考虑了具有分组解释变量的线性模型。这个想法是在假设组数与样本大小具有相同顺序的情况下执行未知系数的不同连续组的自动检测。标准最小二乘损失函数和分位数损失函数都与融合和自适应融合惩罚一起使用，以同时估计和分组未知参数。对所获得的估计量给出了合适的收敛速度，并推导出了不同连续组数的上限。模拟研究用于比较所提出的融合估计器和自适应融合估计器的经验性能，空气质量数据的实际应用证明了所提出方法的实际适用性。