Linear Quantile Regression Research Articles

Biparietal diameter vs crown-rump length as standard parameter for late first-trimester pregnancy dating.

To compare the precision of biparietal diameter (BPD) and crown-rump length (CRL) as predictors of gestational age in the human fetus in the late first and early second trimesters, using a population-based approach. We constructed term and gestational-age prediction curves for first-trimester dating, based on 11 041 pregnancies with 12 260 measurements of CRL and/or BPD from a population-based Norwegian clinical database. We used a population-based approach with local linear quantile regression, combined with a time-to-event strategy that compensates for induced births. Term prediction precision was assessed by estimating and comparing the prediction residual curves using a time-to-event analysis. Individual differences in gestational-age predictions from CRL and BPD were assessed using measurements performed on the same fetus on the same day. A sensitivity analysis was performed to evaluate the effect of not distinguishing between non-spontaneous and spontaneous births. CRL and BPD provided almost identical term prediction precision judged from the residual distribution. In about 51% of examinations, the difference in predicted gestational age was 1 day or less; 24% of examinations had a difference of 2 days, 14% had a difference of 3 days, 7% had a difference of 4 days and only 5% of all examinations had a difference of 5 days or more. Incorrectly removing induced births from the analysis, or treating them as spontaneous, would cause a substantial systematic prediction bias of about 2 days. Based on population data, using comparisons at an individual level, our study found that BPD is as precise as CRL when used for first-trimester dating. BPD has advantages from a clinical point of view, since it is technically less challenging and less time-consuming to measure compared with CRL, and can be measured and assessed throughout the entire pregnancy. © 2024 The Author(s). Ultrasound in Obstetrics & Gynecology published by John Wiley & Sons Ltd on behalf of International Society of Ultrasound in Obstetrics and Gynecology.

Functional quantile regression with missing data in reproducing kernel Hilbert space

We, in this article, focus on functional partially linear quantile regression, where the observations are missing at random, which allows the response or covariates or response and covariates simultaneously missing. Estimation of the unknown function is done based on reproducing kernel method. Under suitable assumptions, we discuss consistency with rates of the estimators, and establish asymptotic normality of the estimator for the parameter. At the same time, we study hypothesis test of the parameter, and prove asymptotic distributions of restricted estimators of the parameter and test statistic under null hypothesis and local alternative hypothesis, respectively. Also, we study variable selection of the linear part of the model. By simulation and real data, finite sample performance of the proposed methods is analyzed.

On function-on-function linear quantile regression

We present two innovative functional partial quantile regression algorithms designed to accurately and efficiently estimate the regression coefficient function within the function-on-function linear quantile regression model. Our algorithms utilize functional partial quantile regression decomposition to effectively project the infinite-dimensional response and predictor variables onto a finite-dimensional space. Within this framework, the partial quantile regression components are approximated using a basis expansion approach. Consequently, we approximate the infinite-dimensional function-on-function linear quantile regression model using a multivariate quantile regression model constructed from these partial quantile regression components. To evaluate the efficacy of our proposed techniques, we conduct a series of Monte Carlo experiments and analyze an empirical dataset, demonstrating superior performance compared to existing methods in finite-sample scenarios. Our techniques have been implemented in the ffpqr package in .

Unified specification tests in partially linear quantile regression models

We propose specification tests for parametric quantile regression models versus semiparametric alternatives over a continuum of quantile levels. The test statistics are constructed as continuous functionals of a quantile-marked residual process. We show that using an orthogonal projection on the tangent space of nuisance parameters at each quantile index delivers unified asymptotic properties for tests based on different estimators. Consistency of the tests and asymptotic power under a sequence of local alternatives converging to the null at a parametric rate are also discussed. We propose a simple multiplier bootstrap procedure to carry out the tests, whose nominal levels are well approximated in our simulation study for modest sample sizes.

Electronic media exposure, parental language input, and child vocalizations in rural and peri-urban China

To examine the association between electronic media exposure and parental language input, Language Environment Analysis technology was used to collect data on electronic media exposure and parental language input in 158 peri-urban and rural households with children aged 18–24 months in southwestern China. The sounds children made and the sounds they heard were quantified. Multiple linear regression and quantile linear regression were used to determine the relationship between electronic media and the outcomes of interest. The results showed that each hour of electronic media exposure was associated with reduced conversational turn count (p < .05) and child vocalization count (p < .05). A large share of the reduction was driven by the higher quantile of children. Reductions associated with electronic exposure were also observed in number of segments and conversational turns. These results may help explain the association between child electronic media exposure and language delay in an under-studied and at-risk population.

Revealing accuracy in climate dynamics: enhancing evapotranspiration estimation using advanced quantile regression and machine learning models

This study examines the effectiveness of various quantile regression (QR) and machine learning (ML) methodologies developed for analyzing the relationship between meteorological parameters and daily reference evapotranspiration (ETref) across diverse climates in Iran spanning from 1987 to 2022. The analyzed models include D-vine copula-based quantile regression (DVQR), multivariate linear quantile regression (MLQR), Bayesian model averaging quantile regression (BMAQR), as well as machine learning algorithms such as extreme learning machine (ELM), random forest (RF), M5 model Tree (M5Tree), least squares support vector regression algorithm (LSSVR), and extreme gradient boosting (XGBoost). Additionally, empirical equations (EEs) such as Baier and Robertson (BARO), Jensen and Haise (JEHA), and Penman (PENM) models were considered. While the EEs demonstrated acceptable performance, the QR and ML models exhibited superior accuracy. Among these, the MLQR model displayed the highest accuracy compared to DVQR and BMAQR models. Moreover, LSSVR, XGBoost, and M5Tree models outperformed ELM and RF models. Notably, LSSVR, XGBoost, and MLQR models exhibited comparable performance (R2 and NSE > 0.92, MBE and RMSE < 0.5, and SI > 0.05) to M5Tree and BMAQR models across all climates. Importantly, these models significantly outperformed EEs, DVQR, ELM, and RF models in all climates. In conclusion, high-dimensional QR and ML models are recommended as promising alternatives for accurately estimating daily ETref in diverse global climate conditions.

Statistical inference for linear quantile regression with measurement error in covariates and nonignorable missing responses

Statistical inference for linear quantile regression with measurement error in covariates and nonignorable missing responses

Taylor Approximation of Inventory Policies for One-Warehouse, Multi-Retailer Systems with Demand Feature Information

We consider a distribution system in which retailers replenish perishable goods from a warehouse, which, in turn, replenishes from an outside source. Demand at each retailer depends on exogenous features and a random shock, and unfulfilled demand is lost. The objective is to obtain a data-driven replenishment and allocation policy that minimizes the average inventory cost per time period. The extant data-driven methods either cannot guarantee a feasible solution for out-of-sample feature observations or generate one with excessive computational time. We propose a policy that resolves these issues in two steps. In the first step, we assume that the distributions of features and random shocks are known. We develop an effective heuristic policy by using Taylor expansion to approximate the retailer’s inventory cost. The resulting solution is closed-form, referred to as Taylor Approximation (TA) policy. We show that the TA policy is asymptotically optimal in the number of retailers. In the second step, we apply the linear quantile regression and kernel density estimation to the TA solution to obtain the data-driven policy called Data-Driven Taylor Approximation (DDTA) policy. We prove that the DDTA policy is consistent with the TA policy. A numerical study shows that the DDTA policy is very effective. Using a real data set provided by Fresh Hema, we show that the DDTA policy reduces the average cost by 11.0% compared with Hema’s policy. Finally, we show that the main results still hold in the cases of correlated demand features, positive lead times, and censored demand. This paper was accepted by J. George Shanthikumar, data science. Funding: Y. Yang acknowledges financial support from the NSFC [Grants 72125004, 71821002]. W. Zhou acknowledges financial support from the NSFC [Grants 72192823, 71821002]. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2021.04241 .

Semi-Functional Partial Linear Quantile Regression Model with Randomly Censored Responses

Semi-Functional Partial Linear Quantile Regression Model with Randomly Censored Responses

Bat Hibernation: In Groups or Individually?

This study focuses on the hibernation behavior of the western barbastelle bat (Barbastella barbastellus) in underground systems in Poland from 2006 to 2011, specifically during the peak hibernation months of December to February. The impact of climate parameters, namely temperature (T), humidity (Rh), and air flow velocity (v), on the clustering behavior of bats during hibernation was investigated. The climate parameters varied within specific ranges: T fluctuated between 6.0 and 12.4 °C, Rh ranged from 56.4 to 91.8%, and v varied from 0.01 to 1.17 m/s. The quantile linear regression method for statistical analysis of the results was employed. This study found that certain combinations of climate parameters influenced the grouping behavior of bats during hibernation. The model structural parameters revealed the following relationships: 1. An increase in the product of T and v led to an increase in the bats’ group size. 2. For pairs of variables such as T and Rh, and Rh and v, an increase in their product resulted in a decrease in the bats’ group size. 3. When considering the product of T, Rh, and v, a decrease in the bats’ group size was also observed.

Treatable mortality and health care related factors across European countries.

Despite the improvements in European health systems, a large number of premature deaths are attributable to treatable mortality. Men make up the majority of these deaths, with a significant gap existing between women and men's treatable mortality rate in the EU. This study aims to identify the healthcare-related factors, including health expenditures, human and physical resources, and hospital services use associated with treatable mortality in women and men across European countries during the period 2011-2019. We use Eurostat data for 28 EU countries in the period 2011-2019. We estimate a panel data linear regression with country fixed effects and quantile linear regression for men and women. The results found (i) differences in drivers for male and female treatable mortality, but common drivers hold the same direction for both sexes; (ii) favorable drivers are GDP per capita, health expenditures, number of physicians per capita, and (only for men) the average length of a hospital stay, (iii) unfavorable drivers are nurses and beds per capita, although nurses are not significant for explaining female mortality. Policy recommendations may arise that involve an improvement in hospital bed management and the design of more specific policies aimed at healthcare professionals.

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.

Quantile Regression in Survival Analysis: Comparing Check-Based Modeling and the Minimum Distance Approach

Introduction: Quantile regression is a valuable alternative for survival data analysis, enabling flexible evaluations of covariate effects on survival outcomes with intuitive interpretations. It offers practical computation and reliability. However, challenges arise when applying quantile regression to censored data, particularly for upper quantiles. The minimum distance approach, utilizing dual-kernel estimation and the inverse cumulative distribution function, shows promise in addressing these challenges, especially with higher-dimensional covariates.&#x0D; Methods: This study contrasts two methods within the realm of quantile linear regression for survival analysis: check-based modeling and the minimum distance approach. Effectiveness is assessed across various scenarios through comprehensive simulation.&#x0D; Results: The simulation results showed that using the quantile regression model with the minimum distance approach reduces the percentage of root mean square error in parameter estimation compared to the quantile regression models based on the check loss function. Additionally, a larger sample size and reduced censoring percentage led to decreased root mean square error in parameter estimation.&#x0D; Conclusion: The research highlights the benefits of using the minimum distance approach for quantile regression. It reduces errors, improves model predictions, captures patterns, and optimizes parameters even with complete data. However, this approach has limitations. The accuracy of estimated quantiles can be influenced by the choice of distance metric and weighting scheme. The assumption of independence between censoring mechanism and survival time may not hold in real-world scenarios. Additionally, dealing with large datasets can be computationally complex.&#x0D; &#x0D;

PARTIALLY FUNCTIONAL LINEAR QUANTILE REGRESSION WITH MEASUREMENT ERRORS.

Ignoring measurement errors in conventional regression analyses can lead to biased estimation and inference results. Reducing such bias is challenging when the error-prone covariate is a functional curve. In this paper, we propose a new corrected loss function for a partially functional linear quantile model with function-valued measurement errors. We establish the asymptotic properties of both the functional coefficient and the parametric coefficient estimators. We also demonstrate the finite-sample performance of the proposed method using simulation studies, and illustrate its advantages by applying it to data from a children obesity study.

Enhancing the reliability of probabilistic PV power forecasts using conformal prediction

The increasing integration of renewable energy, particularly solar photovoltaic (PV) power, presents challenges for power system operation. Accurate forecasts of renewable energy are both financially beneficial for electricity suppliers and necessary for grid operators to optimize operation and avoid grid imbalances. This paper proposes a forecasting framework to implement conformal prediction (CP) on top of point prediction models, which predict the PV power on a day-ahead basis, to quantify the uncertainty of those predictions. Simple and multiple linear regression, along with random forest regression, are used to construct the point predictions based on weather forecasts. Several variants of CP, including weighted CP, CP with k-nearest neighbors (KNN), CP with Mondrian binning, and conformal predictive systems, are built to transform the point predictions into rigorous uncertainty intervals or cumulative distribution functions to enhance reliability. The framework’s performance is evaluated using large datasets of weather predictions and PV power output in the Netherlands. Results indicate that CP combined with KNN and/or Mondrian binning after a linear regressor outperforms the corresponding linear quantile regressor. CP with KNN and Mondrian binning after using random forest regression demonstrates the most accurate probabilistic PV power forecasts, improving the weighted interval score by 14% compared to multiple linear quantile regression.

The Embodiment of Digital Art Elements in Traditional Cultural and Creative Product Designs

Abstract In order to extract the image path of traditional cultural and creative items, we set the binary image target of such products to be black and the backdrop to be white in this research. We followed the use of image vectorization processing technology. In order to address the issue of edge jaggedness in the traditional cultural and creative product image path extraction process, polygonal contour fitting is utilized to optimize the image paths of these products, resulting in the creation of a vector map of these products. The PCA point cloud alignment technique is used, based on the vector map of traditional cultural and creative products, to identify the attributes of these items and build a model of their traditional cultural and creative product design that incorporates digital art. After choosing dependent and independent variables, traditional cultural and creative product design, including digital art aspects, is studied and analyzed using linear quantile regression. The findings demonstrate that all of the value-added ratio’s coefficients are significant and bigger at the 0.2 and 0.95 quantile points, suggesting that raising the ratio can aid in the merger of digital art and more established creative and cultural sectors. The medium (M=3.586) and small standard deviation of the traditional cultural and creative items incorporating digital art suggest that the use function and cost-effectiveness of these products have a stronger influence on purchase motivation. This research encourages the fusion of digital art components with conventional cultural and artistic output in order to give traditional culture a fresh lease of life in the information era.

SUBSAMPLING INFERENCE FOR NONPARAMETRIC EXTREMAL CONDITIONAL QUANTILES

This paper proposes a subsampling inference method for extreme conditional quantiles based on a self-normalized version of a local estimator for conditional quantiles, such as the local linear quantile regression estimator. The proposed method circumvents difficulty of estimating nuisance parameters in the limiting distribution of the local estimator. A simulation study and empirical example illustrate usefulness of our subsampling inference to investigate extremal phenomena.

Quantile Loss Function Empowered Machine Learning Models for Predicting Carotid Arterial Blood Flow Characteristics

This research presents a novel approach using machine learning models with the quantile loss function to predict blood flow characteristics, specifically the wall shear stress, in the common carotid artery and its bifurcated segments, the internal and external carotid arteries. The dataset for training these models was generated through a numerical model developed for the idealized artery. This model represented blood as an incompressible Newtonian fluid and the artery as an elastic pipe with varying material properties, simulating different flow conditions. The findings of this study revealed that the quantile linear regression model is the most reliable in predicting the target variable, i.e., wall shear stress in the common carotid artery. On the other hand, the quantile gradient boosting algorithm demonstrated exceptional performance in predicting wall shear stress in the bifurcated segments. Through this study, the blood velocity and the wall shear stress in the common carotid artery are identified as the most important features affecting the wall shear stress in the internal carotid artery, while the blood velocity and the blood pressure affected the same in the external carotid artery the most. Furthermore, for a given record of the feature dataset, the study revealed the efficacy of the quantile linear-regression model in capturing a possible prevalence of atherosclerotic conditions in the internal carotid artery. But then, it was not very successful in identifying the same in the external carotid artery. However, due to the use of idealized conditions in the study, these findings need comprehensive clinical verification.

From Immunosenescence to Aging Types-Establishing Reference Intervals for Immune Age Biomarkers by Centile Estimation.

Immunological aging type definition requires establishing reference intervals from the distribution of immunosenescence biomarkers conditional on age. For 1605 individuals (18-97 years), we determined the comprehensive immune age index IMMAX from flow-cytometry-based blood cell sub-populations and identified age-specific centiles by fitting generalized additive models for location, scale, and shape. The centiles were uncorrelated with age and facilitated the categorization of individuals as immunologically slow or fast aging types. Using its 50th percentile as a reference, we rescaled the IMMAX to equivalent years of life (EYOL) and computed the immunological age gap as the difference between EYOL and chronological age. Applied to preliminary baseline and follow-up measurements from 53 participants of the Dortmund Vital Study (Clinical-Trials.gov Identifier: NCT05155397), the averaged changes in the IMMAX and EYOL conformed to the 5-year follow-up period, whereas no significant changes occurred concerning IMMAX centiles and age gap. This suggested that the participants immunologically adapted to aging and kept their relative positions within the cohort. Sex was non-significant. Methodical comparisons indicated that future confirmatory analyses with the completed follow-up examinations could rely on percentile curves estimated by simple linear quantile regression, while the selection of the immunosenescence biomarker will greatly influence the outcome, with IMMAX representing the preferable choice.

Fast optimization methods for high-dimensional row-sparse multivariate quantile linear regression

Sparse quantile regression is a useful tool for variable selection, robust estimation and heteroscedasticity treatment in high-dimensional data analysis. Due to the non-smooth of quantile loss, the computation is heavier than the least square models. In the literature, there are various numerical methods for linear quantile regression, such as ADMM developed in Gu et al. [Technometrics. 2017;60(3):319–331]. However, the computation of multivariate quantile regression has not yet been fully resolved, especially when the dimension is high. Motivated by this, we will focus on the design of fast numerical algorithms for row-sparse multivariate quantile regression model. By virtue of proximal operator and Majorize–Minimization, four smoothed algorithms are designed. For all the obtained algorithms, we analyse their convergence and the parameter selection. We conduct plenty of simulations and four real data sets analysis. Finally, we conclude that the smoothed method is faster than the non-smooth method, especially when the number of predictors is large.