Additive models with autoregressive symmetric errors based on penalized regression splines

Oliveira, Rodrigo Arruda de; Paula, Gilberto A.

doi:10.1007/s00180-021-01106-2

Cited by 5 publications

(2 citation statements)

References 23 publications

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“…Therefore, these models offer better flexibility for modeling data than those using only a parametric approach. Semiparametric structures have been effectively utilized to represent nonlinear components, as demonstrated in previous studies such as [1,[14][15][16][17][18][19][20][21]. Based on our literature review, it appears that no semiparametric quantile regression models based on log-symmetric distributions have been developed thus far.…”

Section: Introductionmentioning

confidence: 86%

Modeling Environmental Pollution Using Varying-Coefficients Quantile Regression Models under Log-Symmetric Distributions

Sánchez,

Ibacache-Pulgar,

Marchant

et al. 2023

Axioms

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Many phenomena can be described by random variables that follow asymmetrical distributions. In the context of regression, when the response variable Y follows such a distribution, it is preferable to estimate the response variable for predictor values using the conditional median. Quantile regression models can be employed for this purpose. However, traditional models do not incorporate a distributional assumption for the response variable. To introduce a distributional assumption while preserving model flexibility, we propose new varying-coefficients quantile regression models based on the family of log-symmetric distributions. We achieve this by reparametrizing the distribution of the response variable using quantiles. Parameter estimation is performed using a maximum likelihood penalized method, and a back-fitting algorithm is developed. Additionally, we propose diagnostic techniques to identify potentially influential local observations and leverage points. Finally, we apply and illustrate the methodology using real pollution data from Padre Las Casas city, one of the most polluted cities in Latin America and the Caribbean according to the World Air Quality Index Ranking.

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Section: Introductionmentioning

confidence: 86%

Modeling Environmental Pollution Using Varying-Coefficients Quantile Regression Models under Log-Symmetric Distributions

Sánchez,

Ibacache-Pulgar,

Marchant

et al. 2023

Axioms

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show abstract

“…As a result, practitioners do not even know what ρ range is numerically safe to attempt. Secondly, a PLS solver is often a computational kernel for more advanced smoothing problems, like robust smoothing with M-estimators (Dreassi et al, 2014;Osorio, 2016) and backfitting-based generalized additive models (Eilers and Marx, 2002;Oliveira and Paula, 2021;Hernando Vanegas and Paula, 2016). In these problems, a PLS needs be solved in each iteration for reweighted data and it is more difficult to pre-specify a search interval because it changes from iteration to iteration.…”

Section: Introductionmentioning

confidence: 99%

Automatic Search Interval for Smoothing Parameter in Penalized Splines

Li¹,

Cao²

2022

Preprint

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The selection of smoothing parameter is central to estimation of penalized splines. The best parameter value is often the one that optimizes a smoothness selection criterion, like the minimizer of generalized cross-validation error (GCV) and the maximizer of restricted likelihood (REML). To avoid ending up with an undesired local extremum rather than the global extremum, grid search should be used for optimization. Unfortunately, the method requires a pre-specified search interval that contains the unknown global extremum and there has not been any theory on how it could be provided. As a result, practitioners have to find it by trial and error. To overcome such difficulty, we develop novel algorithms to automatically find this interval. Our automatic search interval has four advantages. (i) It specifies a smoothing parameter range where the penalized least squares problem is numerically solvable. (ii) It is criterion-independent, so that different criteria like GCV and REML can be explored on the same parameter range. (iii) It is sufficiently wide to contain the global extremum of any criterion, so that for example, the global minimum of GCV and the global maximum of REML can both be identified. (iv) It is computationally cheap compared with grid search so that it carries no extra costs in practice. Our method is ready to use through R package gps (>= version 1.1). It may be embedded in other advanced statistical modeling methods that rely on penalized splines.

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Bayesian diagnostics in a partially linear model with first-order autoregressive skew-normal errors

Liu,

Lu,

Paula

et al. 2024

Comput Stat

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Additive models with autoregressive symmetric errors based on penalized regression splines

Cited by 5 publications

References 23 publications

Modeling Environmental Pollution Using Varying-Coefficients Quantile Regression Models under Log-Symmetric Distributions

Modeling Environmental Pollution Using Varying-Coefficients Quantile Regression Models under Log-Symmetric Distributions

Automatic Search Interval for Smoothing Parameter in Penalized Splines

Bayesian diagnostics in a partially linear model with first-order autoregressive skew-normal errors

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