We consider a general monotone regression estimation where we allow for independent and dependent regressors. We propose a modification of the classical isotonic least squares estimator and establish its rate of convergence for the integrated $L^{1}$ -loss function. The methodology captures the shape of the data without assuming additivity or a parametric form for the regression function. Furthermore, the degree of smoothing is chosen automatically and no auxiliary tuning is required for the theoretical analysis. Some simulations and two real data illustrations complement the study of the proposed estimator.

中文翻译：

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用于多元观测的等渗回归估计器的综合 L1 收敛率

我们考虑一般的单调回归估计，其中我们允许独立和相关的回归量。我们提出对经典等张最小二乘估计器的修改，并建立其积分收敛率 $L^{1}$ -损失函数。该方法捕获数据的形状，而无需假设回归函数的可加性或参数形式。此外，平滑程度是自动选择的，理论分析不需要辅助调整。一些模拟和两个真实数据说明补充了对拟议估计器的研究。