Related papers: Non-crossing convex quantile regression
Quantile regression continues to increase in usage, providing a useful alternative to customary mean regression. Primary implementation takes the form of so-called multiple quantile regression, creating a separate regression for each…
In the present paper we investigate the predictive risk of possibly misspecified quantile regression functions. The in-sample risk is well-known to be an overly optimistic estimate of the predictive risk and we provide two relatively simple…
Quantum computers can be considered as a natural means for performing machine learning tasks for inherently quantum labeled data. Many quantum machine learning techniques have been developed for solving classification problems, such as…
This paper considers doing quantile regression on censored data using neural networks (NNs). This adds to the survival analysis toolkit by allowing direct prediction of the target variable, along with a distribution-free characterisation of…
It is well known that quantile regression model minimizes the portfolio extreme risk, whenever the attention is placed on the estimation of the response variable left quantiles. We show that, by considering the entire conditional…
This paper considers the problem of nonparametric quantile regression under the assumption that the target conditional quantile function is a composition of a sequence of low-dimensional functions. We study the nonparametric quantile…
This paper studies large $N$ and large $T$ conditional quantile panel data models with interactive fixed effects. We propose a nuclear norm penalized estimator of the coefficients on the covariates and the low-rank matrix formed by the…
Semiparametric regression offers a flexible framework for modeling non-linear relationships between a response and covariates. A prime example are generalized additive models where splines (say) are used to approximate non-linear functional…
The classical concept of inequality curves and measures is extended to conditional inequality curves and measures and a curve of conditional inequality measures is introduced. This extension provides a more nuanced analysis of inequality in…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
Regression models that go beyond the mean, alongside coherent risk measures, have been important tools in modern data analysis. This paper introduces the innovative concept of Average Quantile Regression (AQR), which is smooth at the…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
This paper studies quantile regression with an endogenous regressor and measurement error in the dependent variable. Standard quantile regression estimators ignoring these two elements can induce substantial bias. We adopt a…
Quantile aggregation with dependence uncertainty has a long history in probability theory with wide applications in finance, risk management, statistics, and operations research. Using a recent result on inf-convolution of quantile-based…
Quantile regression, a robust method for estimating conditional quantiles, has advanced significantly in fields such as econometrics, statistics, and machine learning. In high-dimensional settings, where the number of covariates exceeds…
Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for…
Deep learning has enjoyed tremendous success in a variety of applications but its application to quantile regressions remains scarce. A major advantage of the deep learning approach is its flexibility to model complex data in a more…
In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…
The mainstream theory of hypothesis testing in high-dimensional regression typically assumes the underlying true model is a low-dimensional linear regression model, yet the Box-Cox transformation is a regression technique commonly used to…
Quantile Regression (QR) can be used to estimate aleatoric uncertainty in deep neural networks and can generate prediction intervals. Quantifying uncertainty is particularly important in critical applications such as clinical diagnosis,…