Log‐symmetric quantile regression models

Saulo, Helton; Dasilva, Alan; Leiva, Víctor; Sánchez, Luis; Fuente‐Mella, Hanns de la

doi:10.1111/stan.12243

Cited by 40 publications

(39 citation statements)

References 52 publications

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“…An issue to be further studied is the efficiency of the variables in the securities markets [51,52]. Moreover, generalizations to multivariate models [53], incorporation of temporal [54], spatial [55] and quantile [55,56] regression structures in the modeling, as well as errors in variables [57] and PLS regression [37], should also be considered using the variables: GHSI, country risk, and OECD membership as relevant in relation to countries' economies.…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

Modeling COVID-19 Cases Statistically and Evaluating Their Effect on the Economy of Countries

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COVID-19 infections have plagued the world and led to deaths with a heavy pneumonia manifestation. The main objective of this investigation is to evaluate the performance of certain economies during the crisis derived from the COVID-19 pandemic. The gross domestic product (GDP) and global health security index (GHSI) of the countries belonging–or not–to the Organization for Economic Cooperation and Development (OECD) are considered. In this paper, statistical models are formulated to study this performance. The models’ specifications include, as the response variable, the GDP variation/growth percentage in 2020, and as the covariates: the COVID-19 disease rate from its start in March 2020 until 31 December 2020; the GHSI of 2019; the countries’ risk by default spreads from July 2019 to May 2020; belongingness or not to the OECD; and the GDP per capita in 2020. We test the heteroscedasticity phenomenon present in the modeling. The variable “COVID-19 cases per million inhabitants” is statistically significant, showing its impact on each country’s economy through the GDP variation. Therefore, we report that COVID-19 cases affect domestic economies, but that OECD membership and other risk factors are also relevant.

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Section: Conclusion and Future Researchmentioning

confidence: 99%

Modeling COVID-19 Cases Statistically and Evaluating Their Effect on the Economy of Countries

et al. 2021

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“…A multivariate version of the RBSARMAX model might also be of interest [ 12 , 50 ], and local influence diagnostics could be derived, allowing the detection of potentially influential cases [ 16 ]. Other aspects for future study using this new model are associated with quantile, spatial, partial least squares, principal components, and sampling structures [ 51 , 52 , 53 , 54 , 55 , 56 ].…”

Section: Conclusion Limitations and Future Researchmentioning

confidence: 99%

Modeling Mortality Based on Pollution and Temperature Using a New Birnbaum–Saunders Autoregressive Moving Average Structure with Regressors and Related-Sensors Data

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et al. 2021

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Environmental agencies are interested in relating mortality to pollutants and possible environmental contributors such as temperature. The Gaussianity assumption is often violated when modeling this relationship due to asymmetry and then other regression models should be considered. The class of Birnbaum–Saunders models, especially their regression formulations, has received considerable attention in the statistical literature. These models have been applied successfully in different areas with an emphasis on engineering, environment, and medicine. A common simplification of these models is that statistical dependence is often not considered. In this paper, we propose and derive a time-dependent model based on a reparameterized Birnbaum–Saunders (RBS) asymmetric distribution that allows us to analyze data in terms of a time-varying conditional mean. In particular, it is a dynamic class of autoregressive moving average (ARMA) models with regressors and a conditional RBS distribution (RBSARMAX). By means of a Monte Carlo simulation study, the statistical performance of the new methodology is assessed, showing good results. The asymmetric RBSARMAX structure is applied to the modeling of mortality as a function of pollution and temperature over time with sensor-related data. This modeling provides strong evidence that the new ARMA formulation is a good alternative for dealing with temporal data, particularly related to mortality with regressors of environmental temperature and pollution.

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“…Local influence techniques have been developed for different non-Gaussian and asymmetrical models; see, for example, refs. [16,17,[23][24][25]. As a motivation to develop our work, next, we show the inadequacy of the usual mean regression when analyzing real-world data with an asymmetrical distribution.…”

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confidence: 91%

“…94-125). Based on these two previous considerations, a similar approach to generalized linear models (GLM) can be used for quantile regression; see [15][16][17]. In GLM, the mean is modeled, which is besides one of the parameters of the assumed distribution.…”

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A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications

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Standard regression models focus on the mean response based on covariates. Quantile regression describes the quantile for a response conditioned to values of covariates. The relevance of quantile regression is even greater when the response follows an asymmetrical distribution. This relevance is because the mean is not a good centrality measure to resume asymmetrically distributed data. In such a scenario, the median is a better measure of the central tendency. Quantile regression, which includes median modeling, is a better alternative to describe asymmetrically distributed data. The Weibull distribution is asymmetrical, has positive support, and has been extensively studied. In this work, we propose a new approach to quantile regression based on the Weibull distribution parameterized by its quantiles. We estimate the model parameters using the maximum likelihood method, discuss their asymptotic properties, and develop hypothesis tests. Two types of residuals are presented to evaluate the model fitting to data. We conduct Monte Carlo simulations to assess the performance of the maximum likelihood estimators and residuals. Local influence techniques are also derived to analyze the impact of perturbations on the estimated parameters, allowing us to detect potentially influential observations. We apply the obtained results to a real-world data set to show how helpful this type of quantile regression model is.

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Log‐symmetric quantile regression models

Cited by 40 publications

References 52 publications

Modeling COVID-19 Cases Statistically and Evaluating Their Effect on the Economy of Countries

Modeling COVID-19 Cases Statistically and Evaluating Their Effect on the Economy of Countries

Modeling Mortality Based on Pollution and Temperature Using a New Birnbaum–Saunders Autoregressive Moving Average Structure with Regressors and Related-Sensors Data

A New Quantile Regression Model and Its Diagnostic Analytics for a Weibull Distributed Response with Applications

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