Abstract A novel test statistic is proposed to identify important predictors for the conditional mean function in regression. The stepwise regression algorithm based on the proposed test statistic guarantees variable selection consistency without specifying the functional form of the conditional mean. When the predictors are ultrahigh dimensional, a model-free screening procedure is introduced to precede the stepwise regression algorithm. The screening procedure has the sure screening property when the number of predictors grows at an exponential rate of the available sample size. The finite-sample performances of our proposals are demonstrated via numerical studies.

中文翻译：

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回归中条件均值的无模型变量选择

摘要 提出了一种新的检验统计量来确定回归中条件均值函数的重要预测因子。基于所提出的检验统计量的逐步回归算法保证了变量选择的一致性，而无需指定条件均值的函数形式。当预测变量为超高维时，在逐步回归算法之前引入无模型筛选程序。当预测变量的数量以可用样本大小的指数速率增长时，筛选程序具有确定的筛选特性。我们的提议的有限样本性能通过数值研究得到证明。