A Parametric Quantile Regression Model for Asymmetric Response Variables on the Real Line

Gallardo, Diego I.; Bourguignon, Marcelo; Galarza, Christian E.; Gómez, Héctor W.

doi:10.3390/sym12121938

Cited by 7 publications

(6 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Quantile regression has had intense research activity in recent years for parametric models. See for instance, Galarza et al (2017), Gallardo et al (2020) and Mazucheli et al (2020). However, up to this moment we only find the work of Sánchez et al (2021) related to the application of a BS-type distribution in this context.…”

Section: Distribution K(x) F (X)mentioning

confidence: 66%

Quantile Regression for positive data using a general class of distributions

Gallardo,

Santos-Neto

2021

Preprint

Self Cite

View full text Add to dashboard Cite

This paper presents a general class of quantile regression models for positive continuous data. In this class of models we consider that the response variable has a IRON distribution. We provide inference and diagnostic tools for this class of models. An R package, called IRON, was implemented. This package provides estimation and inference for the parameters and tools useful to check the fit of models. The methods are also illustrated with an application to modeling household income in Chile.

show abstract

Section: Distribution K(x) F (X)mentioning

confidence: 66%

Quantile Regression for positive data using a general class of distributions

Gallardo,

Santos-Neto

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Tian et al [39] discussed the inferences problems of a mixture of linear quantile regression using the EM algorithm. We notice that recently, Gallardo et al [40] introduced a new parametric quantile regression model for asymmetric response variables with a power skew-normal distribution, and Reyes et al [41] proposed a kind of quantile regression model with a generalization of the Student-t distribution as response variables, although these two distributions are different from the asymmetric Laplace distribution in this paper, the ideas of re-parametrization of these two distributions are similar to the mixture representation of ALD.…”

Section: Quantile Regression (Qr) Modelmentioning

confidence: 90%

Robust Procedure for Change-Point Estimation Using Quantile Regression Model with Asymmetric Laplace Distribution

Yang

2023

Symmetry

View full text Add to dashboard Cite

The usual mean change-point detecting method based on normal linear regression is not robust to heavy-tailed data with potential outlying points. We propose a robust change-point estimation procedure based on a quantile regression model with asymmetric Laplace error distribution and develop a non-iterative sampling algorithm from a Bayesian perspective. The algorithm can generate independently and identically distributed samples approximately from the posterior distribution of the position of the change-point, which can be used for statistical inferences straightforwardly. The procedure combines the robustness of quantile regression and the computational efficiency of the non-iterative sampling algorithm. A simulation study is conducted to illustrate the performance of the procedure with satisfying findings, and finally, real data is analyzed to show the usefulness of the algorithm by comparison with the usual change-point detection method based on normal regression.

show abstract

“…Polynomials may tend to overfit in certain areas of the domain spanned by the design vectors. Local overfitting could be mitigated by imposing suitable restrictions such as shape-constraints or specifying particular distributions (e.g., [22,65]). This, however, requires a priori information on the nature of the restrictions and may seriously flaw the modeling results if the imposed restrictions are wrong.…”

Section: Discussionmentioning

confidence: 99%

Quantile Trend Regression and Its Application to Central England Temperature

Haupt

Fritsch

2022

Mathematics

View full text Add to dashboard Cite

The identification and estimation of trends in hydroclimatic time series remains an important task in applied climate research. The statistical challenge arises from the inherent nonlinearity, complex dependence structure, heterogeneity and resulting non-standard distributions of the underlying time series. Quantile regressions are considered an important modeling technique for such analyses because of their rich interpretation and their broad insensitivity to extreme distributions. This paper provides an asymptotic justification of quantile trend regression in terms of unknown heterogeneity and dependence structure and the corresponding interpretation. An empirical application sheds light on the relevance of quantile regression modeling for analyzing monthly Central England temperature anomalies and illustrates their various heterogenous trends. Our results suggest the presence of heterogeneities across the considered seasonal cycle and an increase in the relative frequency of observing unusually high temperatures.

show abstract

A Parametric Quantile Regression Model for Asymmetric Response Variables on the Real Line

Cited by 7 publications

References 17 publications

Quantile Regression for positive data using a general class of distributions

Quantile Regression for positive data using a general class of distributions

Robust Procedure for Change-Point Estimation Using Quantile Regression Model with Asymmetric Laplace Distribution

Quantile Trend Regression and Its Application to Central England Temperature

Contact Info

Product

Resources

About