Search Results (17)

We propose a partially linear regression linear model to explain coffee prices before and after the COVID-19 pandemic. This new regression model incorporates the fundamental assumption of linearity and nonlinearity between these variables. We consider the penalized quasi-likelihood method for parameter estimation and present residual analysis for the new regression model. A simulation study examines penalized quasi-likelihood estimators and the empirical distribution of the quantile residuals. Furthermore, the article aims to identify variables that influence changes in coffee prices, such as the price of Arabica and Robusta varieties, supply (expressed in millions of bags of production), global consumption, exchange rates, inflation, and the pandemic. Full article

This study investigates the dynamic patterns of global financial risk transmission across 11 major economies and four key asset classes (stocks, bonds, foreign exchange, and gold) using daily data spanning 2012 to 2025. To capture the non-linearities of extreme market stress, we construct a multilayer directed network based on least absolute shrinkage and selection operator (LASSO) penalized quantile regression at the 5% lower tail. We estimate tail risk spillovers using a one-year rolling window approach and identify systemically important nodes via an extended PageRank algorithm applied to the resulting adjacency tensors. Empirical results suggest that the rankings of systemically important countries undergo significant re-orderings during crisis periods. We find robust statistical evidence that the Herfindahl–Hirschman Index (HHI) of risk concentration provides forward-looking information regarding structural polarization and systemic fragility. These observed associations remain consistent across alternative quantile thresholds, varying lag lengths, and alternative rolling window specifications. Our results provide granular insights for policymakers monitoring cross-asset contagion and provides a framework for institutional investors to assess potential tail-risk hedging strategies within an increasingly interconnected multilayer architecture. Full article

Since the advent of composite quantile regression (CQR), its inherent robustness has established it as a pivotal methodology for high-dimensional data analysis. High-dimensional outlier contamination refers to data scenarios where the number of observed dimensions (p) is much greater than the sample size (n) and there are extreme outliers in the response variables or covariates (e.g., p/n > 0.1). Traditional penalized regression techniques, however, exhibit notable vulnerability to data outliers during high-dimensional variable selection, often leading to biased parameter estimates and compromised resilience. To address this critical limitation, we propose a novel empirical likelihood (EL)-based variable selection framework that integrates a Bayesian LASSO penalty within the composite quantile regression framework. By constructing a hybrid sampling mechanism that incorporates the Expectation–Maximization (EM) algorithm and Metropolis–Hastings (M-H) algorithm within the Gibbs sampling scheme, this approach effectively tackles variable selection in high-dimensional settings with outlier contamination. This innovative design enables simultaneous optimization of regression coefficients and penalty parameters, circumventing the need for ad hoc selection of optimal penalty parameters—a long-standing challenge in conventional LASSO estimation. Moreover, the proposed method imposes no restrictive assumptions on the distribution of random errors in the model. Through Monte Carlo simulations under outlier interference and empirical analysis of two U.S. house price datasets, we demonstrate that the new approach significantly enhances variable selection accuracy, reduces estimation bias for key regression coefficients, and exhibits robust resistance to data outlier contamination. Full article

We study a novel Doubly penalized ERror Function regularized Quantile Regression (DERF-QR) in this paper. This is a method of variable selection by ERror Function (ERF) regularization in the linear effects model. We introduce a two-stage iterative algorithm combining the iterative reweighted $L_1$ approach and the alternating direction method of multipliers (ADMM) to estimate the model parameters. Numerical simulations show that by using this method we remove redundant variables effectively and obtain accurate coefficient estimations. Our method outperforms two existing penalized quantile regression methods in various error conditions by comparison. Finally, we apply the methodology in a financial dataset and showcase its practicality. Full article

In high-dimensional data analysis, main effects and interaction effects often coexist, especially when complex nonlinear relationships are present. Effective variable selection is crucial for avoiding the curse of dimensionality and enhancing the predictive performance of a model. In this paper, we introduce a nonlinear interaction structure into the additive quantile regression model and propose an innovative penalization method. This method considers the complexity and smoothness of the additive model and incorporates heredity constraints on main effects and interaction effects through an improved regularization algorithm under marginality principle. We also establish the asymptotic properties of the penalized estimator and provide the corresponding excess risk. Our Monte Carlo simulations illustrate the proposed model and method, which are then applied to the analysis of Parkinson’s disease rating scores and further verify the effectiveness of a novel Parkinson’s disease (PD) treatment. Full article

Recently, there has been an increased focus on enhancing the accuracy of machine learning techniques. However, there is the possibility to improve it by selecting the optimal tuning parameters, especially when data heterogeneity and multicollinearity exist. Therefore, this study proposed a statistical model to study the importance of changing the crude oil prices in the European Union, in which it should meet state-of-the-art developments on economic, political, environmental, and social challenges. The proposed model is Elastic-net quantile regression, which provides more accurate estimations to tackle multicollinearity, heavy-tailed distributions, heterogeneity, and selecting the most significant variables. The performance has been verified by several statistical criteria. The main findings of numerical simulation and real data application confirm the superiority of the proposed Elastic-net quantile regression at the optimal tuning parameters, as it provided significant information in detecting changes in oil prices. Accordingly, based on the significant selected variables; the exchange rate has the highest influence on oil price changes at high frequencies, followed by retail trade, interest rates, and the consumer price index. The importance of this research is that policymakers take advantage of the vital importance of developing energy policies and decisions in their planning. Full article

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. Full article

Cumulative evidence has demonstrated that exposure to polycyclic aromatic hydrocarbons (PAHs) or phthalates (PAEs) contributes to a variety of adverse health effects. However, the association of PAHs and PAEs co-exposure with blood cell-based inflammatory indicators during early pregnancy is still unclear. We aimed to investigate the single and mixed associations of exposure to PAHs and PAEs with blood cell-based inflammatory indicators among early pregnant women. A total of 318 early pregnant women were included in this study. General linear regressions were used to estimate the relationships of individual OH-PAHs and mPAEs with blood cell-based inflammatory indicators. The key pollutants were selected by an adapted least absolute shrinkage and selection operator (LASSO) penalized regression model and wasemployed to build the Bayesian kernel machine regression (BKMR) and quantile g-computation (Q-g) models, which can assess the joint association of OH-PAHs and mPAEs with blood cell-based inflammatory indicators. General linear regression indicated that each 1% increase in MOP was associated with a 4.92% (95% CI: 2.12%, 7.68%), 3.25% (95% CI: 0.50%, 6.18%), 5.87% (95% CI: 2.22%, 9.64%), and 6.50% (95% CI: 3.46%, 9.64%) increase in WBC, lymphocytes, neutrophils, and monocytes, respectively. BKMR and Q-g analysis showed that the mixture of OH-PAHs and mPAEs was linked with increased levels of white blood cells (WBC), neutrophils, monocytes, and lymphocytes, and MOP was identified as the dominant contributor. OH-PAHs and mPAEs co-exposure in early pregnancy was associated with elevated blood cell-based inflammatory indicators reactions. More attention should be paid to the inflammation induced by environmental pollution for perinatal women, especially early pregnant women. Full article

The proportional subdistribution hazards (PSH) model is popularly used to deal with competing risks data. Censored quantile regression provides an important supplement as well as variable selection methods due to large numbers of irrelevant covariates in practice. In this paper, we study variable selection procedures based on penalized weighted quantile regression for competing risks models, which is conveniently applied by researchers. Asymptotic properties of the proposed estimators, including consistency and asymptotic normality of non-penalized estimator and consistency of variable selection, are established. Monte Carlo simulation studies are conducted, showing that the proposed methods are considerably stable and efficient. Real data about bone marrow transplant (BMT) are also analyzed to illustrate the application of the proposed procedure. Full article

The continuously increasing GHG emissions have created environmental pollution and several challenges to ecosystems and biodiversity. The challenges of climate change are multipronged, resulting in melting glaciers, flash floods, and severe heat waves. In this regard, the adaptive and mitigation strategies to manage the consequences of climate change are highly important. The transport sector creates a quarter of carbon emissions, and this share is continuously increasing. Accordingly, this research study uses transport competitiveness to determine carbon emissions of the transport sector for 121 countries covering the time period from 2008 to 2018. The Panel Quantile Regression (PQR) technique is engaged to analyze the study results. The findings highlight that transport competitiveness tends to increase carbon emissions of the transport sector across quantile groups 1 and 3, while it reduces carbon emissions in quantile group 2. The U-shaped services’ EKC is validated in quantile groups 2 and 4. The moderation engaged, i.e., transportation competitiveness, changes the turning point of the services’ EKC across quantile groups 2 and 4. However, in the high-CO₂ quantile group, the moderation impact of transport competitiveness is strongest as it reduces the sensitivity by flattening the services’ EKC. Furthermore, the planned expansion of the population and improved institutional quality tend to mitigate carbon emissions across different quantile groups. The policy relevance/implications that are based on the study results/findings are made part of the research paper. Full article

Although the variable selection and regularization procedures have been extensively considered in the literature for the quantile regression $\left(QR\right)$ scenario via penalization, many such procedures fail to deal with data aberrations in the design space, namely, high leverage points (X-space outliers) and collinearity challenges simultaneously. Some high leverage points referred to as collinearity influential observations tend to adversely alter the eigenstructure of the design matrix by inducing or masking collinearity. Therefore, in the literature, it is recommended that the problems of collinearity and high leverage points should be dealt with simultaneously. In this article, we suggest adaptive $LASSO$ and adaptive E-$NET$ penalized $QR$ ($QR$-$ALASSO$ and $QR$-$AE$-$NET$) procedures where the weights are based on a $QR$ estimator as remedies. We extend this methodology to their penalized weighted $QR$ versions of $WQR$-$LASSO$, $WQR$-E-$NET$ procedures we had suggested earlier. In the literature, adaptive weights are based on the RIDGE regression ($RR$) parameter estimator. Although the use of this estimator may be plausible at the ${\ell }_1$ estimator ($QR$ at $\tau =0.5$) for the symmetrical distribution, it may not be so at extreme quantile levels. Therefore, we use a $QR$-based estimator to derive adaptive weights. We carried out a comparative study of $QR$-$LASSO$, $QR$-E-$NET$, and the ones we suggest here, $viz.$, $QR$-$ALASSO$, $QR$-$AE$-$NET$, weighted $QR$$ALASSO$ penalized and weighted $QR$ adaptive $AE$-$NET$ penalized ($WQR$-$ALASSO$ and $WQR$-$AE$-$NET$) procedures. The simulation study results show that $QR$-$ALASSO$, $QR$-$AE$-$NET$, $WQR$-$ALASSO$ and $WQR$-$AE$-$NET$ generally outperform their nonadaptive counterparts. At predictor matrices with collinearity inducing points under normality, the $QR$-$ALASSO$ and $QR$-$AE$-$NET$, respectively, outperform the non-adaptive procedures in the unweighted scenarios, as follows: in all 16 cases (100%) with respect to correctly selected (shrunk) zero coefficients; in 88% with respect to correctly fitted models; and in 81% with respect to prediction. In the weighted penalized $WQR$ scenarios, $WQR$-$ALASSO$ and $WQR$-$AE$-$NET$ outperform their non-adaptive versions as follows: in 75% of the time with respect to both correctly fitted models and correctly shrunk zero coefficients and in 63% with respect to prediction. At predictor matrices with collinearity masking points under normality, the $QR$-$ALASSO$ and $QR$-$AE$-$NET$, respectively, outperform the non-adaptive procedures in the unweighted scenarios as follows: in prediction, in $100\%$ and $88\%$ of the time; with respect to correctly fitted models in $100\%$ and $50\%$ (while in $50\%$ equally); and with respect to correctly shrunk zero coefficients in $100\%$ of the time. In the weighted scenario, $WQR$-$ALASSO$ and $WQR$-$AE$-$NET$ outperform their respective non-adaptive versions as follows; with respect to prediction, both in $63\%$ of the time; with respect to correctly fitted models, in $88\%$ of the time while with respect to correctly shrunk zero coefficients in $100\%$ of the time. At predictor matrices with collinearity inducing points under the t-distribution, the $QR$-$ALASSO$ and $QR$-$AE$-$NET$ procedures outperform their respective non-adaptive procedures in the unweighted scenarios as follows: in prediction, in $100\%$ and $75\%$ of the time; with respect to correctly fitted models $88\%$ of the time each; and with respect to correctly shrunk zero $88\%$ and in $100\%$ of the time. Additionally, the procedures $WQR$-$ALASSO$ and $WQR$-$AE$-$NET$ and their unweighted versions result in the former outperforming the latter in all respective cases with respect to prediction whilst there is no clear "winner" with respect to the other two measures. Overall, the $WQR$-$ALASSO$ generally outperforms all other models with respect to all measures. At the predictor matrix with collinearity-masking points under the t-distribution, all adaptive versions outperformed their respective non-adaptive versions with respect to all metrics. In the unweighted scenarios, the $QR$-$ALASSO$ and $QR$-$AE$-$NET$ dominate their non-adaptive versions as follows: in prediction, in $63\%$ and $75\%$ of the time; with respect to correctly fitted models, in $100\%$ and $38\%$ (while in $62\%$ equally); in $100\%$ of the time with respect to correctly shrunk zero coefficients. In the weighted scenarios, all adaptive versions outperformed their non-adaptive versions as follows: $62\%$ of the time in both respective cases with respect to prediction while it is vice-versa with respect to correctly fitted models and with respect to correctly shrunk zero coefficients. In the weighted scenarios, $WQR$-$ALASSO$ and $WQR$-$AE$-$NET$ dominate their respective non-adaptive versions as follows; with respect to correctly fitted models, in $62\%$ of the time while with respect to correctly shrunk zero coefficients in $100\%$ of the time in both cases. At the design matrix with both collinearity and high leverage points under the heavy-tailed distributions (t-distributions with $d\in (1;6)$ degrees of freedom) scenarios, the dominance of the adaptive procedures over the non-adaptive ones is again evident. In the unweighted scenarios, the procedures $QR$-$ALASSO$ and $QR$-$AE$-$NET$ outperform their non-adaptive versions as follows; in prediction, in $75\%$ and $62\%$ of the time; with respect to correctly fitted models, they perform better in $100\%$ and $88\%$ of the time, while with respect to correctly shrunk zero coefficients, they outperform their non-adaptive ones $100\%$ of the time in both cases. In the weighted scenarios, $WQR$-$ALASSO$ and $WQR$-$AE$-$NET$ dominate their non-adaptive versions as follows; with respect to prediction, in $100\%$ of the time in both cases; and with respect to both correctly fitted models and correctly shrunk zero coefficients, they both do $88\%$ of the time. Results from applications of the suggested procedures to real life data sets are more or less in line with the simulation studies results. Full article

Alternating Direction Method of Multipliers (ADMM) is a widely used machine learning tool in distributed environments. In the paper, we propose an ADMM-based differential privacy learning algorithm (FDP-ADMM) on penalized quantile regression for distributed functional data. The FDP-ADMM algorithm can resist adversary attacks to avoid the possible privacy leakage in distributed networks, which is designed by functional principal analysis, an approximate augmented Lagrange function, ADMM algorithm, and privacy policy via Gaussian mechanism with time-varying variance. It is also a noise-resilient, convergent, and computationally effective distributed learning algorithm, even if for high privacy protection. The theoretical analysis on privacy and convergence guarantees is derived and offers a privacy–utility trade-off: a weaker privacy guarantee would result in better utility. The evaluations on simulation-distributed functional datasets have demonstrated the effectiveness of the FDP-ADMM algorithm even if under high privacy guarantee. Full article

This paper constructs the double penalized expectile regression for linear mixed effects model, which can estimate coefficient and choose variable for random and fixed effects simultaneously. The method based on the linear mixed effects model by cojoining double penalized expectile regression. For this model, this paper proposes the iterative Lasso expectile regression algorithm to solve the parameter for this mode, and the Schwarz Information Criterion (SIC) and Generalized Approximate Cross-Validation Criterion (GACV) are used to choose the penalty parameters. Additionally, it establishes the asymptotic normality of the expectile regression coefficient estimators that are suggested. Though simulation studies, we examine the effects of coefficient estimation and the variable selection at varying expectile levels under various conditions, including different signal-to-noise ratios, random effects, and the sparsity of the model. In this work, founding that the proposed method is robust to various error distributions at every expectile levels, and is superior to the double penalized quantile regression method in the robustness of excluding inactive variables. The suggested method may still accurately exclude inactive variables and select important variables with a high probability for high-dimensional data. The usefulness of doubly penalized expectile regression in applications is illustrated through a case study using CD4 cell real data. Full article

Energy conservation in buildings has increasingly become a hot issue for the Chinese government. Compared to deterministic load prediction, probabilistic load forecasting is more suitable for long-term planning and management of building energy consumption. In this study, we propose a probabilistic load-forecasting method for daily and weekly indoor load. The methodology is based on the long short-term memory (LSTM) model and penalized quantile regression (PQR). A comprehensive analysis for a time period of a year is conducted using the proposed method, and back propagation neural networks (BPNN), support vector machine (SVM), and random forest are applied as reference models. Point prediction as well as interval prediction are adopted to roundly test the prediction performance of the proposed model. Results show that LSTM-PQR has superior performance over the other three models and has improvements ranging from 6.4% to 20.9% for PICP compared with other models. This work indicates that the proposed method fits well with probabilistic load forecasting, which could promise to guide the management of building sustainability in a future carbon neutral scenario. Full article

The single-index model is an intuitive extension of the linear regression model. It has been increasingly popular due to its flexibility in modeling. In this work, we focus on the estimators of the parameters and the unknown link function for the single-index model in a high-dimensional situation. The SCAD and Laplace error penalty (LEP)-based penalized composite quantile regression estimators, which could realize variable selection and estimation simultaneously, are proposed; a practical iterative algorithm is introduced to obtain the efficient and robust estimators. The choices of the tuning parameters, the bandwidth, and the initial values are also discussed. Furthermore, under some mild conditions, we show the large sample properties and oracle property of the SCAD and Laplace penalized composite quantile regression estimators. Finally, we evaluated the performances of the proposed estimators by two numerical simulations and a real data application. Full article