Dynamic Quantile Linear Models: A Bayesian Approach

Gonçalves, Kelly C. M.; Migon, Hélio S.; Bastos, Leonardo Soares

doi:10.1214/19-ba1156

Cited by 13 publications

(8 citation statements)

References 59 publications

(71 reference statements)

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“…Under the Bayesian approach, West and Harrison (1997) capture the time variation by using the DLM. Gonçalves et al (2018) present a quantile regression model using the DLM applied to an asymmetric Laplace distribution.…”

Section: A Dynamic Quantile Regression For the Gev Modelmentioning

confidence: 99%

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Bayesian time‐varying quantile regression to extremes

Nascimento

Bourguignon

2019

Environmetrics

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Maximum analysis consists of modeling the maximums of a data set by considering a specific distribution. Extreme value theory (EVT) shows that, for a sufficiently large block size, the maxima distribution is approximated by the generalized extreme value (GEV) distribution. Under EVT, it is important to observe the high quantiles of the distribution. In this sense, quantile regression techniques fit the data analysis of maxima by using the GEV distribution. In this context, this work presents the quantile regression extension for the GEV distribution. In addition, a time‐varying quantile regression model is presented, and the important properties of this approach are displayed. The parameter estimation of these new models is carried out under the Bayesian paradigm. The results of the temperature data and river quota application show the advantage of using this model, which allows us to estimate directly the quantiles as a function of the covariates. This shows which of them influences the occurrence of extreme temperature and the magnitude of this influence.

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Section: A Dynamic Quantile Regression For the Gev Modelmentioning

confidence: 99%

“…Kozumi and Kobayashi (2011) show the case in which the sampling can be performed using Gibbs sampling. Gonçalves, Migon, and Bastos (2018) consider a dynamic linear model (DLM) in the quantile regression, where the parameters vary over time.…”

Section: Introductionmentioning

confidence: 99%

Bayesian time‐varying quantile regression to extremes

Nascimento

Bourguignon

2019

Environmetrics

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“…To surpass the adverse effect due to the presence of outliers, various robust linear models have been proposed in the literature. Cantoni and Ronchetti (2001) puts forth the concept of robust deviances that can be used for step-wise model selection; McKean (2004) uses the robust analysis which is based on a fit based on norms other than ℓ 2 ; Lô and Ronchetti (2009) proposes robust test statistic for hypothesis testing and variable selection in GLM; Valdora and Yohai (2014) robustifies the generalized linear models by using M-estimators after applying variance stabilizing transformations; Wang and Blei (2018) and Gonçalves et al (2020) take Bayesian approach. Some other related works in robustifying the GLMs include (Lee and Nelder, 2003;Jearkpaporn et al, 2005;Ghosh and Basu, 2016).…”

Section: Introductionmentioning

confidence: 99%

Robust Linear Predictions: Analyses of Uniform Concentration, Fast Rates and Model Misspecification

Chakraborty¹,

Paul²,

Das³

2022

Preprint

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The problem of linear predictions has been extensively studied for the past century under pretty generalized frameworks. Recent advances in the robust statistics literature allow us to analyze robust versions of classical linear models through the prism of Median of Means (MoM). Combining these approaches in a piecemeal way might lead to ad-hoc procedures, and the restricted theoretical conclusions that underpin each individual contribution may no longer be valid. To meet these challenges coherently, in this study, we offer a unified robust framework that includes a broad variety of linear prediction problems on a Hilbert space, coupled with a generic class of loss functions. Notably, we do not require any assumptions on the distribution of the outlying data points (O) nor the compactness of the support of the inlying ones (I). Under mild conditions on the dual norm, we show that for misspecification level ǫ, these estimators achieve an error rate of O(max |O| 1/2 n −1/2 , |I| 1/2 n −1 + ǫ), matching the best-known rates in literature. This rate is slightly slower than the classical rates of O(n −1/2 ), indicating that we need to pay a price in terms of error rates to obtain robust estimates. Additionally, we show that this rate can be improved to achieve so-called "fast rates" under additional assumptions.

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“…Yet another approach is to propose the variances of high quantiles over time through a structure of dynamic models. Gonçalves, Migon & Bastos (2019) presented this approach for quantile regression, whereas Nascimento, Gamerman & Lopes (2016) performed the modeling for GPD parameters. Furthermore, Huerta & Sansó (2007) presented this approach for GEV, where it was possible to obtain any quantile p variances over time through a unique model.…”

Section: Introductionmentioning

confidence: 99%

Extreme Value Theory Applied to r Largest Order Statistics Under the Bayesian Approach

Silva

Nascimento

2019

Rev. colomb. estad.

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Extreme Value Theory Applied to r r r Largest Order Statistics Under the Bayesian ApproachTeoría de valores extremos aplicada a las r r r estadísticas de orden superior desde el punto de vista bayesiano Abstract Extreme value theory (EVT) is an important tool for predicting efficient gains and losses in economic and environmental domains. Moreover, EVT was initially developed for use with normal and gamma parametric distribution patterns. However, economic and environmental data present a heavy-tailed distribution in most cases, which is in contrast with the above patterns. Thus, the framing of extreme events using EVT presented great difficulties. Furthermore, it is nearly impossible to use conventional models to make predictions about non-observed events that exceeded the maximum number of observations. In some situations, EVT is used to analyze only the maximum values of a given dataset, which provides few observations. In such cases, it is more effective to use the r largest order statistics. This study proposes Bayesian estimators for the parameters of the r largest order statistics. We use a Monte Carlo simulation to analyze the experimental data and observe certain estimator properties, such as mean, confiance interval, credibility interval, bias, and root mean square error (RMSE); estimation provided inferences for these parameters and return levels. In addition, this study proposes a procedure for selecting the r-optimal of the r largest order statistics based on the Bayesian approach and applying the Markov chains Monte Carlo (MCMC) method. Simulation results reveal that the Bayesian approach produced performance similar to that of the maximum likelihood estimation. Finally, the applications developed using the Bayesian approach showed a gain in accuracy compared with other estimators. ResumenLa teoría de valores extremos (EVT) es una herramienta importante para predecir ganancias y pérdidas eficientes en ambientes económicos y ambientales. Además, la EVT se desarrolló inicialmente para uso con patrones de distribución paramétricos normales y gamma. Sin embargo, los datos económicos y ambientales presentan una distribución de cola pesada en la mayoría de los casos, lo que contrasta con los patrones anteriores. Así, la formulación de eventos extremos con EVT presenta grandes dificultades. Además, es casi imposible usar modelos convencionales para obtener predicciones sobre eventos no observados que excedieron el número máximo de observaciones. En algunas situaciones, EVT es utilizado para analizar solamente los valores máximos de un conjunto de datos dado, que proporcionan poca información. En tales casos, es más eficiente usar las r estadísticas de orden superior. Este trabajo propone estimadores bayesianos para los parámetros de las r estadísticas de orden superior. Utilizamos simulaciónes de Monte Carlo para analizar los datos experimentales y observar ciertas propiedades del estimador como: media, intervalos de confianza y credibilidad, sesgo y error cuadrático medio (RMSE). Este tipo de estimación p...

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Dynamic Quantile Linear Models: A Bayesian Approach

Cited by 13 publications

References 59 publications

Bayesian time‐varying quantile regression to extremes

Bayesian time‐varying quantile regression to extremes

Robust Linear Predictions: Analyses of Uniform Concentration, Fast Rates and Model Misspecification

Extreme Value Theory Applied to r Largest Order Statistics Under the Bayesian Approach

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