Related papers: Quantile regression with generalized multiquadric …
Censored quantile regression (CQR) has become a valuable tool to study the heterogeneous association between a possibly censored outcome and a set of covariates, yet computation and statistical inference for CQR have remained a challenge…
Functional data such as curves and surfaces have become more and more common with modern technological advancements. The use of functional predictors remains challenging due to its inherent infinite-dimensionality. The common practice is 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,…
Functional quantile regression (FQR) is a useful alternative to mean regression for functional data as it provides a comprehensive understanding of how scalar predictors influence the conditional distribution of functional responses. In…
To make inferences about the shape of a population distribution, the widely popular mean regression model, for example, is inadequate if the distribution is not approximately Gaussian (or symmetric). Compared to conventional mean regression…
In this paper, we develop a quantile functional regression modeling framework that models the distribution of a set of common repeated observations from a subject through the quantile function, which is regressed on a set of covariates to…
We show that the estimating equations for quantile regression can be solved using a simple EM algorithm in which the M-step is computed via weighted least squares, with weights computed at the E-step as the expectation of independent…
In ordinary quantile regression, quantiles of different order are estimated one at a time. An alternative approach, which is referred to as quantile regression coefficients modeling (QRCM), is to model quantile regression coefficients as…
We propose Multivariate Quantile Function Forecaster (MQF$^2$), a global probabilistic forecasting method constructed using a multivariate quantile function and investigate its application to multi-horizon forecasting. Prior approaches are…
We propose a prediction procedure for the functional linear quantile regression model by using partial quantile covariance techniques and develop a simple partial quantile regression (SIMPQR) algorithm to efficiently extract partial…
Linear Regression is a seminal technique in statistics and machine learning, where the objective is to build linear predictive models between a response (i.e., dependent) variable and one or more predictor (i.e., independent) variables. In…
Quantile regression is a powerful statistical methodology that complements the classical linear regression by examining how covariates influence the location, scale, and shape of the entire response distribution and offering a global view…
The Multi-Kink Quantile Regression (MKQR) model is an important tool for analyzing data with heterogeneous conditional distributions, especially when quantiles of response variable are of interest, due to its robustness to outliers and…
This paper studies the inference problem in quantile regression (QR) for a large sample size $n$ but under a limited memory constraint, where the memory can only store a small batch of data of size $m$. A natural method is the na\"ive…
In the regression problem, L1 and L2 are the most commonly used loss functions, which produce mean predictions with different biases. However, the predictions are neither robust nor adequate enough since they only capture a few conditional…
This paper considers the quantile regression approach for partially linear spatial autoregressive models with possibly varying coefficients. B-spline is employed for the approximation of varying coefficients. The instrumental variable…
We investigate an empirical quantile estimation approach to solve chance-constrained nonlinear optimization problems. Our approach is based on the reformulation of the chance constraint as an equivalent quantile constraint to provide…
Quantile is a popular performance measure for a stochastic system to evaluate its variability and risk. To reduce the risk, selecting the actions that minimize the tail quantiles of some loss distributions is typically of interest for…
We link conditional generative modelling to quantile regression. We propose a suitable loss function and derive minimax convergence rates for the associated risk under smoothness assumptions imposed on the conditional distribution. To…
Due to the dynamic nature of financial markets, maintaining models that produce precise predictions over time is difficult. Often the goal isn't just point prediction but determining uncertainty. Quantifying uncertainty, especially the…