Quantile Estimation Research Articles

Simple & Optimal Quantile Sketch: Combining Greenwald-Khanna with Khanna-Greenwald

Estimating the ε-approximate quantiles or ranks of a stream is a fundamental task in data monitoring. Given a stream x_1,..., x_n from a universe \mathcalU with total order, an additive-error quantile sketch \mathcalM allows us to approximate the rank of any query y\in \mathcalU up to additive ε n error. In 2001, Greenwald and Khanna gave a deterministic algorithm (GK sketch) that solves the ε-approximate quantiles estimation problem using O(ε^-1 łog(ε n)) space \citegreenwald2001space ; recently, this algorithm was shown to be optimal by Cormode and Vesleý in 2020 \citecormode2020tight. However, due to the intricacy of the GK sketch and its analysis, over-simplified versions of the algorithm are implemented in practical applications, often without any known theoretical guarantees. In fact, it has remained an open question whether the GK sketch can be simplified while maintaining the optimal space bound. In this paper, we resolve this open question by giving a simplified deterministic algorithm that stores at most (2 + o(1))ε^-1 łog (ε n) elements and solves the additive-error quantile estimation problem; as a side benefit, our algorithm achieves a smaller constant factor than the \frac11 2 ε^-1 łog(ε n) space bound in the original GK sketch~\citegreenwald2001space. Our algorithm features an easier analysis and still achieves the same optimal asymptotic space complexity as the original GK sketch. Lastly, our simplification enables an efficient data structure implementation, with a worst-case runtime of O(łog(1/ε) + łog łog (ε n)) per-element for the ordinary ε-approximate quantile estimation problem. Also, for the related "weighted'' quantile estimation problem, we give efficient data structures for our simplified algorithm which guarantee a worst-case per-element runtime of O(łog(1/ε) + łog łog (ε W_n/w_\textrmmin )), achieving an improvement over the previous upper bound of \citeassadi2023generalizing.

A new approach to estimate parameters of the two-parameter Weibull distribution

This study proposes a new approach to estimate the parameters of the two-parameter Weibull distribution in the case of complete (uncensored) or doubly Type II censored samples. The proposed estimators have closed forms and can be adapted to Type II right or Type II left censored samples. The new estimators are strongly consistent and the new shape estimator follows asymptotically a normal and the new scale estimator a lognormal distribution. Bias, mean square and efficiency performance of the new estimators are investigated through simulations and compared to some known estimation methods such as maximum likelihood estimation, method of moments, quantile estimation, maximum goodness of fit estimation, L-moments, U-statistics and bias-corrected maximum likelihood. According to the simulations, the newly proposed estimators seem to have good efficiency performance in comparison to the other methods, particularly in small samples. Furthermore, two real data sets are used to illustrate the new estimators.

A Nonlinear Quantile Regression for Accelerated Destructive Degradation Testing Data

Traditional regression approaches to accelerated destructive degradation test (ADDT) data have modeled the mean curve as representative. However, maximum likelihood estimates (MLEs) of the mean model are likely to be biased when the data are non-Gaussian or highly skewed. The median model can be an alternative for skewed degradation data. In this work, we introduce a nonlinear quantile regression (QR) approach for estimating quantile curves of ADDT data. We propose an iterative QR algorithm that uses the generalized expectation-maximization (GEM) framework to estimate the parameters of the nonlinear QR ADDT model, based on the asymmetric Laplace distribution to accommodate non-Gaussian and skewed errors. Using the asymptotic properties of the QR parameter estimates, we estimate variance-covariance matrix for the τ th QR parameters using order statistics and bootstrap methods. We propose a new prediction method of the quantile of the failure-time distribution in the normal use condition. Confidence intervals for the quantiles of the failure-time distribution are constructed using the parametric bootstrap method. The proposed model is illustrated using an industrial application and compared with the existing model. Various quantile curve estimates derived using the QR ADDT model provide a more flexible modeling framework than the traditional mean ADDT modeling approach.

The Bahadur Representation for Empirical and Smooth Quantile Estimators Under Association

The Bahadur Representation for Empirical and Smooth Quantile Estimators Under Association

Macroeconomic Environment and Stock Price Movement in Nigeria: An Evaluation of Fama’s Model of Efficient Market

The study examined the link between macroeconomic environmental dynamics and stock price movements in Nigeria using Fama’s model of efficient market approach. The macroeconomic climate posed issues for Nigerian stock markets. The buying power of local currency occasionally impacted unfavourable changes in the majority of macroeconomic variables. In this study, an ex post facto research design was used. The study looked at certain macroeconomic variables and the evolution of Nigerian stock prices between 1985 and 2021. To test the hypothesis, quantile regression estimates of the Fama-French three-factor coefficient were derived. The findings showed that the interest rate and stock price movement have a negative and negligible association. Additionally, a strong and positive correlation was observed between the exchange rate and changes in stock prices. It was recommended that in order to promote stock market activity and, by extension, enhance stock prices in Nigeria, a suitable monetary policy and a sufficient amount of money supply must be implemented. Also, well-diversified portfolios that mirror the entire market portfolio should be recommended to investors to protect themselves against stock price volatility. This would serve as a guide to protect them against shocks resulting from the macroeconomic environment.

Do non-linearity and non-Gaussianity truly matter in streamflow forecasting? A comparative study between PAR(p) and vine copula for Brazilian streamflow time series.

This study evaluates the joint impact of non-linearity and non-Gaussianity on predictive performance in 23 Brazilian monthly streamflow time series from 1931 to 2022. We consider point and interval forecasting, employing a PAR(p) model and comparing it with the periodic vine copula model. Results indicate that the Gaussian hypothesis assumed by PAR(p) is unsuitable; gamma and log-normal distributions prove more appropriate and crucial for constructing accurate confidence intervals. This is primarily due to the assumption of the Gaussian distribution, which can lead to the generation of confidence intervals with negative values. Analyzing the estimated copula models, we observed a prevalence of the bivariate Normal copula, indicating that linear dynamic dependence is frequent, and the Rotated Gumbel 180°, which exhibits lower tail dependence. Overall, the temporal dynamics are predominantly shaped by combining these two types of effects. In point forecasting, both models show similar behavior in the estimation set, with slight advantages for the copula model. The copula model performs better during the out-of-sample analysis, particularly for certain power plants. In interval forecasting, the copula model exhibits pronounced superiority, offering a better estimation of quantiles. Consistently demonstrating proficiency in constructing reliable and accurate intervals, the copula model reveals a notable advantage over the PAR(p) model in interval forecasting.

Examining the impact of personal freedom on income inequality: Evidence from Sub-Saharan Africa and Western European regions.

Rising income inequality has recently garnered intensive attention owing to its significance in theory and practice. This has rendered the mechanism through which inequality can be understood, even from a microscopic perspective, to institute proper policies that curtail it important. We contribute to the literature by examining the effect of freedom on income inequality using data from 34 least-free and 18 most-free countries from 2000 to 2020 in Sub-Saharan Africa and Western Europe, respectively. A novel fixed-effects panel quantile regression econometric estimator was employed, and the findings showed a non-linear relationship between personal freedom and income inequality for both regions. Again, both regions reported an inverse relationship between personal freedom and income inequality within the medium-run quantiles. However, a positive relationship was reported in the short-run and long-run quantiles of Sub-Saharan Africa and Western Europe, respectively, whereas the inverse was the same. Finally, the significant adverse relationship was more dominant in Western Europe, implying that high levels of personal freedom in the region explain the low levels of income inequality compared to Sub-Saharan Africa, which has lower levels of personal freedom and higher income inequality. Concerning the findings, it is recommended that policymakers and governments of least- and most-free regions institutionalise personal liberties that support human capital development and establish mechanisms to implement enacted freedoms.

Trade policy and environmental sustainability in Africa: An empirical analysis

AbstractThis study investigates whether trade policy instruments—tariffs—strengthen or worsen African environmental sustainability. To drive out the objectives of the study, fully modified ordinary least square (FMOLS), dynamic OLS (DOLS), augmented mean group (AMG), method of moment quantile regression (MMQR) and Dumitrescu–Hurlin panel causality approaches are used to analyse the effect of tariff in addition to other control variables on carbon and ecological footprints as measured of environmental sustainability from 2001 to 2020. The results from the MMQR reveal that tariffs have a significant positive effect on carbon footprints in the 0.15 quantile, while the effect becomes insignificant between 0.25 and 0.5 quantiles. However, at the upper quantiles level (0.75–0.95), the impact of the tariff on carbon footprint is negative and significant, with increasing coefficients. Furthermore, tariffs significantly positively affect lower and middle quantiles' ecological footprints (0.15–0.5). However, the effect turns negative at the upper quantiles (0.9 and 0.95), suggesting that tariff reduces ecological footprint at these levels. In addition, the long‐run estimates (FMOLS, DOLS and AMG) also support the upper quantile estimates of MMQR. A one‐way causality between tariffs, carbon and ecological footprint was found. These findings reveal that tariffs do not create market inefficiency in Africa. This study recommends that tariffs as a trade policy instrument could be used to strengthen Africa's environmental quality. The government can use the tariff revenue to subsidize cleaner production and consumption and move the economy from a traditional energy source to renewable energy.

Developing Non-Stationary Frequency Relationships for Greater Pamba River basin, Kerala India incorporating dominant climatic precursors

Abstract. Global climate changes significantly contribute to increased frequency of hydrologic extremes. This significantly underestimates the hydrologic design parameters, bringing of hydro systems to increased failure risk. In order to address this concern, the current practice of development of hydrologic frequency tools need to be updated accounting for non-stationarity. This study first considered a diverse set of statistical tests to examine the trend, change points, non-stationarity and randomness of streamflow, rainfall and temperature time series of scales ranging from daily to annual. The annual maxima time series indicated non stationarity against the stationary behaviour of daily series of hydro-meteorological datasets of the basin. Subsequently, this study developed the Temperature Duration Frequency (TDF), Rainfall Intensity Duration Frequency (IDF) and Flood Frequency (FF) curves of Greater Pamba river basin in Kerala India, the part of which was most severely affected by the near century return period flood event of 2018. The analysis was performed for a multitude of combinations of variations in distribution parameters with time and climatic drivers as physical covariates in the extreme value formulations. The study proposed a novel wavelet coherence (WC) based driver selection of most dominant combination of climatic precursors in developing FF and IDF relations of three locations of Kalloopara, Malakkara and Thumpamon and TDF curve of Kuttanad region in the basin, considering data of 1985–2015 period. The proposed WC framework considers bi-multi-and partial effects of climatic oscillations (COs) like El Niño Southern Oscillation (ENSO), Indian Ocean Dipole (IOD), Pacific Decadal Oscillation (PDO) and North Atlantic Oscillation (NAO) in identifying potential drivers. The different WC formulations captured in-phase relationships of streamflows and rainfall with COs at intra-annual, annual and inter annual scales up to 4 years. The methods showed that addition of climatic precursors improved the NS estimates of flood and rainfall quantiles by more accurately capturing the magnitudes of extreme streamflows and rainfalls of 2018, 2021 than the time covariate formulations. However, the role of COs on extreme temperature is not found to be influential in developing TDF relationships, which needs further investigation.

Searching for homogeneous regions in regional flood frequency analysis for Southeast Australia

Study regionSoutheast Australia Study focusThis study examines identification of homogeneous regions for regional flood frequency analysis (RFFA) using 201 gauged catchments and applying principal component analysis (PCA) and cluster analysis. Quantile regression technique (QRT) is applied to develop prediction equations. Leave-one-out (LOO) validation is used to evaluate the accuracy of the developed prediction equations. New hydrologic insights for the regionFor the regions formed based on PCA and cluster analysis, the Hosking and Wallis’ heterogeneity (H1) statistics are found to vary in the range of 11.55–24.52, and 5.11–26.27, respectively. The assumed regions are highly heterogeneous as H1 values are much higher than 1.00. The median of absolute relative error values associated with the developed prediction equations for the assumed regions are found to vary in the range of 17–62 %, which are comparable to similar RFFA studies. PCA and cluster analysis do not deliver sufficiently homogeneous regions in southeast Australia. The degree of heterogeneity of a region has little effect on the relative accuracy of flood quantile estimates. The findings of this study will assist to update RFFA technique in Australian Rainfall and Runoff (national guideline).

Generative Quantile Regression with Variability Penalty

Quantile regression and conditional density estimation can reveal structure that is missed by mean regression, such as multimodality and skewness. In this article, we introduce a deep learning generative model for joint quantile estimation called Penalized Generative Quantile Regression (PGQR). Our approach simultaneously generates samples from many random quantile levels, allowing us to infer the conditional distribution of a response variable given a set of covariates. Our method employs a novel variability penalty to avoid the problem of vanishing variability, or memorization, in deep generative models. Further, we introduce a new family of partial monotonic neural networks (PMNN) to circumvent the problem of crossing quantile curves. A major benefit of PGQR is that it can be fit using a single optimization, thus, bypassing the need to repeatedly train the model at multiple quantile levels or use computationally expensive cross-validation to tune the penalty parameter. We illustrate the efficacy of PGQR through extensive simulation studies and analysis of real datasets. Code to implement our method is available at https://github.com/shijiew97/PGQR.

Summarizing quantile estimates of weight at length to compare condition: Geographic and temporal variation in Arctic Grayling

AbstractObjectiveWe developed a novel, simple approach to summarize variation in quantile regression estimates of weight at length across multiple levels of grouping factors (locations or years) and demonstrate its utility for comparing fish condition using Arctic Grayling Thymallus arcticus data. We compared condition among 28 geographic locations of Arctic Grayling populations and among 12 and 25 years for two populations.MethodsWe summarized variation among locations and among years within locations using percentiles (maximum, 75th, 50th, 25th, and minimum) of predicted quantiles of weight at length, allowing us to simplify the distributions of predicted quantiles of weight into highest to lowest fourths (quartiles) across locations or years. One part of this summary information, 75th percentiles of median (0.50 quantile) predicted weights at length across populations, is identical to summary statistics used to develop standard weight equations for computing relative weights. However, our approach avoids biases inherent in fitting a single standard weight equation and can accommodate among‐fish variation in weight at length via multiple quantiles when developing reference standards for comparative or diagnostic purposes. A selected new weight at length can be compared with the distribution of quantile predictions among locations in terms of weights or as proportionate weights similar to relative weight.ResultArctic Grayling in 28 geographic locations, from the southern limit of their distribution in Montana and Wyoming north through Canada and Alaska to the Arctic coast, had considerable variation in allometric exponents in weight–length relationships and in predicted weights at length. Predicted weights of Arctic Grayling for heavier fish (0.90 quantiles) in populations with less (lower quartiles) to greater (upper quartiles) weights were 127–194 g and 336–510 g at total lengths = 250 and 350 mm, respectively. Lighter fish (0.10 quantiles) in populations with less to greater weights were 100–133 g and 259–364 g, at the same total lengths, respectively. We provide statistical code and tabled values that can be used as reference standards as a replacement for standard weight equations for comparing new samples of fishes. We also quantified annual variation in condition within two intensively sampled populations, the Kuparuk River in Alaska (25 years, 1985–2012) and Red Rock Creek, Montana (12 years, 1994–2016). Annual distributions of weights at length were greater for Arctic Grayling in Red Rock Creek than those in the Kuparuk River. Variation in predicted distributions of weights at length among years was also greater for Red Rock Creek, although fish from both locations exhibited substantial among‐year variation that exceeded half the variation estimated among geographic locations.ConclusionOur estimates indicated that there was substantial spatial and temporal variation in condition of Arctic Grayling that might be investigated further to help understand constraints on populations to aid conservation and management of the species. Our summary approach can be easily extended to other investigations of fish weight at length relationships where multiple quantile estimates are made across many levels of grouping factors.

Bayesian Quantile Regression Models for Complex Survey Data Under Informative Sampling

Abstract The interest in considering the relation among random variables in quantiles instead of the mean has emerged in various fields, and data collected from complex survey designs are of fundamental importance to different areas. Despite the extensive literature on survey data analysis and quantile regression models, research papers exploring quantile regression estimation accounting for an informative design have primarily been restricted to a frequentist framework. In this paper, we introduce different Bayesian methods relying on the survey-weighted estimator and the estimating equations. A model-based simulation study evaluates the proposed methods compared to alternative approaches and a naïve model fitting ignoring the informative sampling design under different scenarios. In addition, we illustrate and conduct a prior sensitivity analysis in a design-based simulation study that uses data from Prova Brasil 2011.

How do technology convergence and expansibility affect information technology diffusion? Evidence from the internet of things technology in China

Information technology diffusion (ITD) is essential for promoting the sustainable development of technologies and helping technology owners gain a competitive advantage. The web-based development of technology and the digital transformation needs of multidisciplinary markets simultaneously drive the increasing convergence and expansibility of information technology (IT). However, whether these two technological characteristics can contribute to the diffusion of early-stage IT and how they influence the further diffusion of IT that has already diffused on a large scale are yet to be thoroughly investigated. We argue that the impact of technology convergence on ITD is heterogeneous when distinguishing between low- and high-ITD scenarios, as is technology expansibility. Our quantile regression estimates use a dataset about Internet of Things (IoT) patents authorized by the Chinese Patent Office from 2009 to 2019. The results show that increased technology convergence benefits ITD in high-ITD scenarios but does not affect ITD in low-ITD scenarios. Technology expansibility negatively impacts ITD in high-ITD scenarios and positively impacts ITD in low-ITD scenarios. This study broadens the theoretical paradigm of “technological characteristics and ITD” from the domain perspective. It inspires information technology owners to formulate sustainable strategies related to ITD according to technology convergence and expansibility.

Some practical and theoretical issues related to the quantile estimators

The paper contains the comparative analysis of the efficiency of different qunatile estimators for various distributions. Additionally, we show strong consistency of different quantile estimators and we study the Bahadur representation for each of the quantile estimators, when the sample is taken from NA, φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi $$\\end{document}, ρ∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho ^*$$\\end{document}, ρ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho $$\\end{document}-mixing population.

Quantile-based sequential optimization and reliability assessment method under random and interval hybrid uncertainty

Under random and interval hybrid uncertainties, solving hybrid reliability based design optimization (HRBDO) can acquire an optimal balance between structural performance and reliability. Since solving HRBDO includes a triple nested framework involving minimum analysis of performance function (PF), failure probability constraint analysis and design parameter optimization, the computational complexity of HRBDO is high, especially for dealing with complex structures. Therefore, a quantile-based sequential optimization and reliability assessment method (QSORA) is proposed for reducing the computational complexity of HRBDO. In the proposed QSORA for HRBDO, failure probability constraint is firstly transformed into minimum PF (MPF) quantile one corresponding to target failure probability. Then, approximating the difference between PF and its target quantile at current iteration by that at previous one, the failure probability constraint analysis is decoupled from the design parameter optimization. Moreover, by approximating the minimum point of the PF with respect to the interval input in the current iteration by that in the previous one, the minimum analysis of PF is separated from the design parameter optimization. By the separation of minimum analysis and failure probability constraint analysis from the design parameter optimization in the proposed QSORA, the triple nested framework of HRBDO is decoupled sequentially as the deterministic design optimization, the minimum analysis of the PF and the target MPF quantile estimation, and this way of reconstructing the HRBDO from the triple nested framework to three single-loop frameworks can significantly enhance the efficiency of solving HRBDO. Furthermore, the MPF quantile at the current design parameter is estimated by stochastic collocation based statistical moment method, in which the stochastic collocation method is employed to efficiently estimate the MPF moment to approximate the probability density function of MPF. The efficiency and accuracy of the QSORA are validated by four numerical and engineering examples finally.

Regional event-based flood quantile estimation method for large climate projection ensembles

Emerging large ensemble climate datasets produced by multiple general circulation models and their downscaling products challenge the limits of hydrodynamic models because of the immense data size. To overcome this new challenge and estimate the discharge quantiles corresponding to different return periods at all river sections in an entire region, this study proposes an event-based regional approach that uses a nationwide distributed rainfall–runoff model as well as large climate projection ensembles. This approach addresses the high computational burden associated with continuous simulations and solves the problem of conventional event-based simulations serving only a single outlet of a basin. For our analysis, we extracted 372 annual maximum 48 h rainfall events that cover the entirety of Shikoku Island and its eight major river basins. Peak discharges were estimated using a 150 m resolution rainfall–runoff–inundation model. These discharges were then screened using either the peak-over-threshold (POT) method or block maxima (BM) method, and frequency curves were subsequently constructed and evaluated. The primary reason for the necessity of POT or BM was to avoid interference from extraneous low discharges. The POT-based frequency curves showed good accuracy when using peak discharges in the range of the top 10–50%, and the results remain stable within this threshold range. The BM method, employing block sizes of 2–5 years, can generate relatively accurate frequency curves, but the choice of block size introduces significant variations in results among certain basins. Generally, the accuracy of results based on the POT method surpasses that of the BM method. Considering the accuracy, computational cost, and result stability, the POT method is preferred. The error introduced by the regional approach was acceptable with more than half of the relative root-mean-square errors remaining within 10% and basically all of the results are within 20%. The results of the regional approach exhibited good accuracy across climate scenarios and provided consistent information regarding future flood quantiles. This study serves as the foundation for high-resolution future flood risk assessment.

Risk-Conditioned Reinforcement Learning: A Generalized Approach for Adapting to Varying Risk Measures

In application domains requiring mission-critical decision making, such as finance and robotics, the optimal policy derived by reinforcement learning (RL) often hinges on a preference for risk management. Yet, the dynamic nature of risk measures poses considerable challenges to achieving generalization and adaptation of risk-sensitive policies in the context of RL. In this paper, we propose a risk-conditioned RL model that enables rapid policy adaptation to varying risk measures via a unified risk representation, the Weighted Value-at-Risk (WV@R). To sample risk measures that avoid undue optimism, we construct a risk proposal network employing a conditional adversarial auto-encoder and a normalizing flow. This network establishes coherent representations for risk measures, preserving the continuity in terms of the Wasserstein distance on the risk measures. The normalizing flow is used to support non-crossing quantile regression that obtains valid samples for risk measures, and it is also applied to the agent’s critic to ascertain the preservation of monotonicity in quantile estimations. Through experiments with locomotion, finance, and self-driving scenarios, we show that our model is capable of adapting to a range of risk measures, achieving comparable performance to the baseline models individually trained for each measure. Our model often outperforms the baselines, especially in the cases when exploration is required during training but risk-aversion is favored during evaluation.

A quantile shift approach to main effects and interactions in a 2-by-2 design

When comparing two independent groups, shift functions are basically techniques that compare multiple quantiles rather than a single measure of location, the goal being to get a more detailed understanding of how the distributions differ. Various versions have been proposed and studied. This paper deals with extensions of these methods to main effects and interactions in a between-by-between, 2-by-2 design. Two approaches are studied, one that compares the deciles of the distributions, and one that has a certain connection to the Wilcoxon–Mann–Whitney method. There are many quantile estimators, but for reasons summarized in the paper, the focus is on using the Harrell–Davis quantile estimator used in conjunction with a percentile bootstrap method. Included are results comparing two methods aimed at controlling the probability of one or more Type I errors.

Global economic policy uncertainty and renewable energy demand: Does environmental policy stringency matter? Evidence from OECD economies

Existing literature recommends the essential role of renewable energy consumption (REC) in achieving environmental sustainability. Although prior works have investigated the significant factors of REC, the effect of green environmental policies remains largely understudied, particularly in OECD countries. Therefore, this study specifically examines the role of environmental policy stringency (EPS) in enhancing (or diminishing) REC in 27 OECD economies between 2000 and 2019. Furthermore, we aim to specify the determinants of REC and investigate whether EPS could help moderate the relationship between global economic policy uncertainty (GEPU) and REC. To accomplish this, we employ both the fixed effects and panel quantile estimation methods. The findings underline that EPS has a positive and significant impact on REC, indicating that stricter green environmental policies lead to encouraging REC. Besides, the findings show that EPS has a beneficial role in lessening the negative effect of GEPU on REC, and its negative effect on REC is more moderated as moves from environments with low EPS to high EPS. The results also underscore that financial market development, FDI, remittances, technological innovation, and economic development positively promote REC whereas CO2 and natural resources rents have a detrimental impact. The findings are significant and a wide range of policy suggestions is recommended to governments, policymakers, and regulators to attain the energy and environmental sustainability targets set out in SDG 7 and SDG 13, respectively.