# Quantile Regression Estimation Using Non-Crossing Constraints

@article{Amerise2018QuantileRE, title={Quantile Regression Estimation Using Non-Crossing Constraints}, author={Ilaria Lucrezia Amerise}, journal={Journal of Mathematics and Statistics}, year={2018}, volume={14}, pages={107-118} }

In this article we are concerned with a collection of multiple linear regressions that enable the researcher to gain an impression of the entire conditional distribution of a response variable given a set of explanatory variables. More specifically, we investigate the advantage of using a new method to estimate a bunch of non-crossing quantile regressions hyperplanes. The main tool is a weighting system of the data elements that aims to reduce the effect of contamination of the sampled…

## 3 Citations

### Solution to the Non-Monotonicity and Crossing Problems in Quantile Regression

- EconomicsArXiv
- 2021

A new method to address the long-standing problem of lack of monotonicity in estimation of the conditional and structural quantile function, also known as quantile crossing problem is proposed, based on a single mathematical equation that is easy to understand and implement in R and Python.

### Statistical Properties of the log-cosh Loss Function Used in Machine Learning

- Mathematics, Computer ScienceArXiv
- 2022

A quantile distribution function from which a maximum likelihood estimator for quantile regression can be derived is identified and a quantile M-estimator based on log-cosh with robust monotonicity is compared against another approach to quantiles regression based on convolutional smoothing.

### Calibrated Predictive Distributions via Diagnostics for Conditional Coverage

- Computer ScienceArXiv
- 2022

This work shows that recalibration as well as validation are indeed attainable goals in practice and gives full diagnostics of conditional coverage across the entire feature space and can be used to recalibrate misspecified PDs.

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