Quantile Estimation Research Articles

Alternate pathway for regional flood frequency analysis in data-sparse region

Accurately analyzing flood frequency is crucial for developing effective flood management strategies and designing flood protection infrastructure, but the complex and nonlinear nature of the hydrological system poses significant challenges. The use of advanced statistical techniques, hydrological modeling, and computational tools has facilitated the implementation of several regional flood frequency analysis (RFFA) methods, including machine learning (ML) approaches. However, such regional methods, being statistical and data-intensive with limited hydrologic inferences, can be challenging for regions with limited data. In this study, we evaluated an alternate approach or path for RFFA in two contrasting regions: a data-sparse region in India and a data-dense region in the USA. The alternate approach involves using deep learning (DL)-based model for streamflow prediction, followed by at-site flood frequency analysis to estimate flood quantiles. The proposed alternate approach was compared with the classical RFFA method, which utilized the Random Forest (RF) and eXtreme Gradient Boosting (XGBoost) algorithms to establish the intricate relationship between different flood quantiles and predictor variables related to physio-meteorological conditions. The findings showed that the alternate approach outperformed the classical RFFA method in the data-sparse region of India, reducing the mean absolute error (MAE) and root mean squared error (RMSE) by approximately 50 %, and achieving a higher coefficient of determination (R2 = 0.85 to 0.96). In the data-dense region, the classical and alternate approaches produced comparable results. However, the alternate approach has the benefit of flexibility and offers a complete time series of daily flow at the ungauged watersheds, enabling the estimation of other flow attributes or magnitudes for any return period without needing a separate classical RFFA model. The study demonstrates that the alternate approach can produce reliable flood quantile estimates in regions with limited data, offering a promising solution for managing floods in these areas.

Ultra-short-term wind power probabilistic forecasting based on an evolutionary non-crossing multi-output quantile regression deep neural network

Ultra-short-term wind power probabilistic forecasting is of significance for stable power grid operation; however, it is still challenging due to the inherent nonlinearity and uncertainty. Most state-of-the-art methods have focused on achieving quantile prediction using a combination of linear quantile regression and nonlinear complex deep neural networks. Yet, these methods struggle with several dilemmas. Quantile regression deep neural networks require a complete training once for each quantile. The multi-training mode and complex structure of quantile regression deep neural network can lead to extremely high computational complexity. Most of the training of quantile regression deep neural networks are guided by the loss of each quantile, and the weights are adjusted by gradient descent in which the gradient explosion and quantile crossover may be encountered. Therefore, this paper proposes a non-crossing multi-output quantile regression deep neural network optimized by chaotic particle swarm optimization. It designs a multi-output deep neural network to output all quantile estimations simultaneously through one training, effectively solving the structural complexity problem of traditional quantile regression deep neural networks. Since quantile regression produces a non-differentiable loss function which significantly hinders model training, the proposed neural network is trained by chaotic particle swarm optimization. It not only achieves the effect of optimizing all quantile losses simultaneously, but also can significantly alleviate the dilemma of training in traditional neural network weight optimization. In addition, several non-crossing constraints are designed for avoiding quantile crossover. The proposed model is trained and tested on two real-world wind power case studies. The experiment results show that the proposed model shows superiority in performance criteria, training speed, and avoiding quantile crossover.

Assessing some statistical and physical modelling uncertainties of extreme responses for monopile-based offshore wind turbines, using metocean contours

This study examines the influence of probabilistic models for wave parameters in the joint environmental model and hydrodynamic/soil models on extreme mudline bending moments for monopile-based wind turbines at representative wind speeds, using the environmental contour method. For significant wave height, the 3-parameter Weibull model using the method of moments (MoM) provides the best fit to hindcast data across different wind classes, for the statistical models and data considered in the study. The hybrid Log-normal-Weibull (LonoWe) model also provides a reasonable fit but is sensitive to the transition point between distributions. Both models yield the largest extreme responses, with differences of approximately 0.5–3.5%. The 3-parameter Weibull model with maximum likelihood estimation (MLE) and the 2-parameter Weibull model result in less conservative contours, leading to up to 13% lower extreme responses, compared to LonoWe and Weibull (MoM). Regarding peak period, both the Log-normal and 3-parameter Weibull models provide reasonable fits, with the latter being more accurate near the steepness (breaking) limit. The stochastic variation among maxima due to seed variability and the uncertainty in quantile estimates as a function of number of samples was found to be crucial, particularly for severe sea states at the cut-out speed. Soil modelling is particularly important when the turbine is parked and encounters peak wave periods close to the turbine’s natural periods, while the effect of soil modelling on the extremes during turbine operation is negligible. Additionally, the impact of diffraction becomes relatively important for short wave periods. However, it is worth noting that the choice of load models has less impact on extreme responses compared to variations in the contours caused by different statistical models or seed variability.

Temporal changes in the frequency of flood types and their impact on flood statistics

Standard flood frequency analysis assumes stationarity of flood conditions, i.e., no change of the distribution over time. However, long-term variability in climate and anthropogenic impacts question this assumption. Consequently, more and more non-stationary models are considered in flood frequency analyses. Yet, most of them only consider a change-point or trend in the magnitude of flood peaks while ignoring changes in the underlying flood geneses. Recent climate reports suggest such a change in frequency of certain flood-generating factors, e.g., the increase of frequency of heavy-rainfall events. In this study, flood types are applied to detect changes in the meteorological drivers of flood regimes. By application of a robust change-point test for the variance based on Gini’s Mean Difference, significant changes in the frequency of occurrence of certain flood types are detected. A clear tendency to more frequent heavy-rainfall floods and less snowmelt-induced floods is observed for many catchments in Central Europe. A special focus is laid on the shifts in winter floods, which occur less often and are replaced by rainfall-driven floods. The impacts of such changes on flood statistics are demonstrated by several approaches. Though the magnitude of flood peaks does not (necessarily) change, the changing frequency of floods leads to changing flood quantiles. Quantile estimations from traditional statistical analyses of annual series are compared to results of type-based flood statistics. It is shown how standard models are more affected by these changes because they are not able to compensate for changes in the frequency of individual flood types.

Quasi-maximum Likelihood Inference for Linear Double Autoregressive Models

This paper investigates the quasi-maximum likelihood inference including estimation, model selection and diagnostic checking for linear double autoregressive (DAR) models, where all asymptotic properties are established under only fractional moment of the observed process. We propose a Gaussian quasi-maximum likelihood estimator (G-QMLE) and an exponential quasi-maximum likelihood estimator (E-QMLE) for the linear DAR model, and establish the consistency and asymptotic normality for both estimators. Based on the G-QMLE and E-QMLE, two Bayesian information criteria are proposed for model selection, and two mixed portmanteau tests are constructed to check the adequacy of fitted models. Moreover, we compare the proposed G-QMLE and E-QMLE with the existing doubly weighted quantile regression estimator in terms of the asymptotic efficiency and numerical performance. Simulation studies illustrate the finite-sample performance of the proposed inference tools, and a real example on the Bitcoin return series shows the usefulness of the proposed inference tools.

Quantile estimators for regression errors in mixture models with varying concentrations

In this paper we consider data obtained from a mixture of M different sub-populations (mixture components). Dependencies between the observed variables are described by nonlinear regression models with unknown regression parameters and error terms distributions different for different components. The mixing probabilities (concentrations of the components in the mixture) vary from observation to observation. Estimators for quantiles of error terms distributions are considered based on weighted empirical distribution functions of the regression models residuals. Consistency of these estimators is demonstrated. The results can be applied to the construction of quantile vs. quantile plots for visual comparison and analysis of error terms distributions.

Modelling an Improved Swarm Optimizer and Boosted Quantile Estimator For Malicious Flow Monitoring And Prediction In Network

For a long time, malware has posed a significant risk to computer system security. The effectiveness of conventional detection techniques based on static and dynamic analysis is restricted due to the quick advancement of anti-detection technologies. In recent years, AI-based malware detection has increasingly been employed to combat malware due to its improved predictive ability. Unfortunately, because malware may be so diverse, it can be challenging to extract features from it, which makes using AI for malware detection ineffective. A malware classifier based on an Improved Salp Swarm optimization for feature selection and a Boosted tree with Conditional Quantile Estimation (ISSO-BCQE) is developed to adapt different malware properties to solve the problem. Specifically, the malware code is extracted, and the feature sequence is generated into a boosting tree where the feature map of the node is extracted using BCQE, where a boosting network is used to design a classifier and the method's performance is finally analyzed and compared. The results show that our model works better than other approaches regarding FPR and accuracy. It also shows that the method beats current methods with the highest accuracy of 99.6% in most detecting circumstances. It is also stable in handling malware growth and evolution.

Quantile estimation in fractional Levy Ornstein-Uhlenbeck processes

First we study estimation of the drift parameter in the fractional Ornstein-Uhlenbeck process whose marginal distribution is Student t-distribution. We obtain Spearman’s correlation based estimator, quantile estimator and Brownian excursion based estimator of the drift parameter. Then we study method of moments estimator and quantile estimator in fractional inverse Gaussian and fractional gamma Ornstein-Uhlenbeck processes.

Role of green innovation and green finance on green recovery: Analysis of natural resources rents

This study examines the relationship between globalization, eco-financing, sustainable expansion, and CO2 emissions in China's economy between 2012 and 2022. The research demonstrates cointegration between variables using complicated estimating methods. Due to the asymmetrical data distribution, the innovative moment quantile regression approach is necessary. According to the results, regional emissions are negatively affected by globalisation, yet there is a favorable association between economic development and CO2 emissions. Also, up to a certain point, the analysis shows that green finance development and economic growth have a positive correlation with CO2 emissions. However, beyond that point, both elements work together to significantly lower emissions. Bootstrap quantile estimation verifies the models' reliability. According to this study, minerals, natural gas, and other natural resources are major sources of carbon dioxide emissions in the area.The current research presents the policy implications of increasing investments in environmentally beneficial finance in light of concrete empirical evidence.

Impact of Financial Integration on Economic Development: A Dynamic Panel Quantile Regression Analysis

This paper investigated the impact of financial integration on economic development using the dynamic panel quantile estimator on a sample of 95 countries from 2004-2019. The results showed that the impact of financial integration on economic development varied across income levels. This study found that financial integration impacted economic development negatively in middle and high-income countries. However, financial integration did not significantly affect economic development in low-income countries.

Functional-Coefficient Quantile Regression for Panel Data with Latent Group Structure

This article considers estimating functional-coefficient models in panel quantile regression with individual effects, allowing the cross-sectional and temporal dependence for large panel observations. A latent group structure is imposed on the heterogeneous quantile regression models so that the number of nonparametric functional coefficients to be estimated can be reduced considerably. With the preliminary local linear quantile estimates of the subject-specific functional coefficients, a classic agglomerative clustering algorithm is used to estimate the unknown group structure and an easy-to-implement ratio criterion is proposed to determine the group number. The estimated group number and structure are shown to be consistent. Furthermore, a post-grouping local linear smoothing method is introduced to estimate the group-specific functional coefficients, and the relevant asymptotic normal distribution theory is derived with a normalization rate comparable to that in the literature. The developed methodologies and theory are verified through a simulation study and showcased with an application to house price data from U.K. local authority districts, which reveals different homogeneity structures at different quantile levels.

The second-order bias and mean squared error of quantile regression estimators

The second-order bias and mean squared error of quantile regression estimators

Sampling Importance Resampling Algorithm with Nonignorable Missing Response Variable Based on Smoothed Quantile Regression

The presence of nonignorable missing response variables often leads to complex conditional distribution patterns that cannot be effectively captured through mean regression. In contrast, quantile regression offers valuable insights into the conditional distribution. Consequently, this article places emphasis on the quantile regression approach to address nonrandom missing data. Taking inspiration from fractional imputation, this paper proposes a novel smoothed quantile regression estimation equation based on a sampling importance resampling (SIR) algorithm instead of nonparametric kernel regression methods. Additionally, we present an augmented inverse probability weighting (AIPW) smoothed quantile regression estimation equation to reduce the influence of potential misspecification in a working model. The consistency and asymptotic normality of the empirical likelihood estimators corresponding to the above estimating equations are proven under the assumption of a correctly specified parameter working model. Furthermore, we demonstrate that the AIPW estimation equation converges to an IPW estimation equation when a parameter working model is misspecified, thus illustrating the robustness of the AIPW estimation approach. Through numerical simulations, we examine the finite sample properties of the proposed method when the working models are both correctly specified and misspecified. Furthermore, we apply the proposed method to analyze HIV—CD4 data, thereby exploring variations in treatment effects and the influence of other covariates across different quantiles.

Estimation of regional and at-site quantiles of extreme winds under flood index procedure

Extreme winds are becoming more common among environmental events with the most catastrophic societal consequences. A regional frequency analysis of Daily Annual Maximum Wind Speed (DAMWS) is necessary not only for a comprehensive understanding of wind hazards but also for infrastructure design and safety, wind energy potential, disaster risk reduction, insurance and risk assessment in a particular region of study. This study investigated regional frequency analysis of DAMWS of Baluchistan and Sindh provinces of Pakistan. L-moments regionalization techniques along with flood index procedure were applied to DAMWS records of 21 stations from 1990 to 2019 across the study area. We intended to find the regional frequency distribution for maximum winds and predict the returns for extreme winds events in the future. Only one station namely Lasbella was found to be discordant. With the help of cluster analysis, the remaining 20 stations were further divided into two homogeneous. Heterogeneity measures validate that both regions are homogenous with allotted stations. Regional quantiles for both regions are estimated through best-fit probability distribution among Generalized Normal (GNO), Generalized Logistic (GLO), Pearson Type 3 (P3), Generalized Pareto (GPA), and Generalized Extreme Value (GEV). Robustness of GLO distribution compared to GEV distribution is assessed through Monte Carlo simulations of relative bias and relative root mean square error. Findings clearly show that GLO distribution is the best for regional modeling. Furthermore, with the help of index flood procedure we determined at-site quantiles of all stations for various return periods. These estimated quantiles are of valuable information for various sectors, including infrastructure, energy, disaster management, and climate resilience, leading to improved planning, development, and risk reduction in the face of wind-related hazards in Sindh and Balochistan provinces of Pakistan.

Labour income share, market power and automation: Evidence from an emerging economy

The macroeconomic implications of movements in labour income share across several economies are of serious concern. This study examines the relationship between labour income share and its key drivers: market power, capital intensity and automation. The study uses data on Indian firms from 2013 to 2021. The relationship is analysed by employing panel fixed effects and method of moments panel quantile estimators. The results indicate that market power is significantly and negatively associated with the labour share of income. Similarly, capital intensity and automation have a positive impact on the labour income share. Estimates of quantile regression reveal that the influence of market power and automation becomes more pronounced at higher quantiles of the labour share. In general, the relationship is consistent even after accounting for firm size and ownership type. The study also indicate complementary nature of labour and capital.

Spatiotemporal Analysis of Ozone Concentration Using Semi-Functional Partial Linear Models

As weather warms up in China, ozone pollution rises to the top of the list of air pollutants. In this research, we examine the spatiotemporal variability of particulate matter components using contemporary functional data analysis techniques. The technique models the yearly pollutant profiles to describe their dynamic behavior over time and location. These cutting-edge methods offer dimension reduction for better data display and permit us to forecast annual profiles for locations and years for which data are lacking. In order to accurately estimate hourly ozone concentrations for 12 stations in China over two years (2015-2016), this study set out to showcase the best prediction models currently available. To accurately predict Ozone concentration, several methods are used, including Kernel Functional Classical Estimation (KFCE), Kernel Functional Quantile estimation (KFQE), Semi-Partial Linear Functional Classical Estimation (SPLFCE), Semi-Partial Linear Functional Quantile Estimation (SPLFQE), and Semi-Partial Linear Functional Expectile Estimation (SPLFEE). These functional models were chosen based on their ability to establish a forecast region with a given level of confidence. In terms of prediction accuracy, we may conclude that the Semi-Partial linear models outperform conventional models.

Dynamic nonlinear effects of geopolitical risks on commodities: Fresh evidence from quantile methods

This paper examines the dynamic nonlinear effects of the Geopolitical Risk (GPR) on commodities using quantile methods. Our rolling window quantile estimations show that non-energy sectors, such as food and beverage, are not easily influenced by geopolitical events, while energy sectors can be easily affected. The recent COVID-19 pandemic has no strong effects on these relationships. Quantile-on-quantile results demonstrate that the magnitude of the co-movement of GPR and non-energy sectors is very small, whereas the magnitude of the co-movement of GPR associated with the energy sector is larger. Additionally, during bullish markets, GPR can exert positive effects on commodity markets. However, under other market conditions, negative effects are apparent. Finally, we use a nonparametric causality-in-quantiles test to provide fresh evidence of the explanatory power of GPR on commodity markets.

Assessment of Minimal Clinically Important Difference in Patient-Reported Myelofibrosis-Associated Symptoms Using an Anchor-Based Analysis Based on MANIFEST Arm 3 Data

Background Myelofibrosis (MF) is a life-threatening hematologic neoplasm that can arise as a primary condition or as a progression from polycythemia vera or essential thrombocythemia. The MF Symptom Assessment Form (MFSAF) v4.0 is a seven-item questionnaire that assesses symptom severity from the patients' (pts) perspective. Each item is rated on a scale from 0 (Absent) to 10 (Worst Imaginable). The MFSAF Total Symptom Score (TSS) ranges from 0 to 70, with higher scores indicating worse symptoms. A ≥50% reduction in TSS (TSS50) is a commonly used binary endpoint in clinical trials. However, the clinical meaningfulness of the dichotomization of response at 50% cutoff across the spectrum of responses remains uncertain. The relevance of considering TSS as a continuous endpoint in MF studies is assessed here to capture the full spectrum of symptom changes, enabling a potentially more accurate assessment of treatment effects. Pelabresib (CPI-0610) is an investigational oral small-molecule BET inhibitor, while the Janus kinase inhibitors (JAKis) ruxolitinib or fedratinib are the current standard of care for intermediate- or high-risk pts with MF.InArm 3 of the Phase 2 MANIFEST trial of JAKi treatment-naïve pts with MF treated with pelabresib and ruxolitinib, 56% achieved TSS50 response at Week (Wk) 24. Aims This anchor-based analysis aims to determine the minimal clinically important difference (MCID) of change in TSS as a continuous endpoint, based on data from JAKi treatment-naïve pts with MF treated with pelabresib and ruxolitinib, to better evaluate the incremental clinical benefit of treatment effects. Methods Data from Arm 3 of the MANIFEST Phase 2 study of treatment-naïve pts with MF treated with pelabresib combined with ruxolitinib were used (July 29, 2022 data cut). Anchor-based methods compare the change in a scale-based outcome measure with that of an established patient-reported outcome (PRO). These methods are commonly used to establish the MCID, defined as the smallest difference in score that pts consider beneficial. In this analysis, the Patient Global Impression of Change (PGIC), a seven-point scale reflecting overall improvement compared with baseline (BL), was used as the anchor PRO. On the PGIC, pts rated their change from ‘very much improved’ to ‘very much worse’ (Table 1). The relationship between TSS changes (percentage and absolute) at Wk 24 and PGIC categories was examined using correlation and graphical analyses. Linear and quantile regressions were applied to assess the impact of a one-point difference in PGIC score on TSS change at Wk 24, adjusting for BL TSS score. Only pts with available TSS and PGIC data at Wk 24 were included, with no imputation for missing values. Results In Arm 3 of the MANIFEST trial, 78 of 84 pts treated with pelabresib and ruxolitinib had complete TSS data and PGIC at Wk 24. At BL, mean TSS was 16.4 (SD=8.4), and median TSS was 15.5 (range 2.0-38.3). A -58.8% and -7.7 median percentage and absolute reduction in TSS at Wk 24 was observed, respectively. For PGIC at Wk 24 (Table 1), only six pts (7.7%) scored in the three worsening PGIC categories. Percentage and absolute changes in TSS, and the percentage TSS50 responders for each PGIC category are shown in Table 1. Linear regression demonstrated that a one-category increase in PGIC (indicating worsening) corresponded to an 11.89% increase (95% CI 3.12-20.65) in TSS (indicating worsening) at Wk 24. The quantile regression estimate for this relationship was 11.36% (3.53-19.19). For absolute change at Wk 24, a one-category increase in PGIC resulted in a 1.67 (range 0.74-2.60) increase in mean TSS, with a 1.87 (range 0.62-3.12) increase in median TSS. Conclusion Assuming a one-category change in the seven-category PGIC represents a clinically meaningful difference, the analyses suggest that the MCID in TSS for JAKi treatment-naïve pts with MF could be approximately 11-12% for percentage change from BL and approximately 1.5-2 points for absolute change from BL. These findings provide valuable guidance for assessing treatment outcomes and evaluating symptom improvements' clinical significance in this patient population. Further exploration of these findings requires larger data sets, which will be addressed in the forthcoming Phase 3 MANIFEST-2 study evaluating pelabresib and ruxolitinib versus placebo and ruxolitinib in JAKi treatment-naïve pts with MF.

Does oil price volatility and financial expenditures of the oil industry influence energy generation intensity? Implications for clean energy acquisition

This study examines the nexus between financial expenditures within the Chinese oil business, the volatility of oil prices, and the energy-generating sector. This research examines Chinese oil and energy industry statistics from 1980 to 2020, drawing upon resource curse and energy transition theories. The results of this study are generated by using correlation analysis, quantile process estimation, autoregressive distributed lag (ARDL), and sensitivity analysis. The nexus among variables is seen across all quantiles, ranging from 22% to 81%. On the contrary, a negative association exists between oil price volatility and industrial financial expenditures, with the magnitude of the correlation ranging from 19% to 90%. Significantly, these connections exhibit statistical significance in short-term and long-term scenarios. This paper proposes implications to enhance financial expenditures in the Chinese oil business. These strategies include diversification, hedging via futures contracts and swaps, and short-term forecasts of oil price movements.

Impact of Public Debt on Economic Growth: A Quantile Regression Approach

This study aimed at investigating the nexus between government debt and its determinants in the context of sustainable economic growth for 97 countries over the period from 2004 to 2018 by employing a panel data quantile regression and comparing it across a fixed-effects model and a generalized method of moments (GMM) model. The different touches of debt on economic growth were analysed. The quantile regression estimates revealed that government debt has various impacts on economic growth, relying on the degree of economic performance. Government debt negatively affects economic growth across all the quantiles. More interestingly, the quantile regression estimates indicated that in countries with a very low level of real GDP per capita growth, government debt has a stronger pernicious effect on economic growth compared to upper-middle and high-income countries. Hence, our results provided insightful information for policy makers in designing appropriate fiscal policies particularly for low- and lower- middle-income countries to mitigate the negative effect on economic growth, and it should be maintained at a low and reasonable level to promote sustainable economic growth. JEL Classification: E61, E62, E63, H63, O4, O40