Title: On Integrated $L^{1}$ Convergence Rate of an Isotonic Regression Estimator for Multivariate Observations,
Abstract: 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.