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We consider a general monotone regression estimation where we allow forindependent and dependent regressors. We propose a modification of theclassical isotonic least squares estimator and establish its rate ofconvergence for the integrated $L_1$-loss function. The methodology capturesthe shape of the data without assuming additivity or a parametric form for theregression function. Furthermore, the degree of smoothing is chosenautomatically and no auxiliary tuning is required for the theoretical analysis.Some simulations and two real data illustrations complement the study of theproposed estimator.

On Integrated $L^{1}$ Convergence Rate of an Isotonic Regression Estimator for Multivariate Observations