# On Integrated L1 Convergence Rate of an Isotonic Regression Estimator for Multivariate Observations

arXiv: https://arxiv.org/abs/1710.04813 · HTML: https://mlsanity.com/paper/1710.04813/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2017.

## Built on by (most cited first, 1 of 1)

- [Differentiable Neural Networks with RePU Activation: with Applications to Score Estimation and Isotonic Regression](https://mlsanity.com/paper/2305.00608/) (2023)

## Abstract (arXiv)

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 L1-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.