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Optimal subsampling for linear quantile regression models

CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 2021年第4期49卷 1039-1057页

作者： Fan, Yan Liu, Yukun Zhu, Lixing Shanghai Univ Int Business & Econ Sch Stat & Informat Shanghai Peoples R China East China Normal Univ Sch Stat KLATASDS MOE Shanghai Peoples R China Beijing Normal Univ Ctr Stat & Data Sci Zhuhai Peoples R China

Subsampling techniques are efficient methods for handling big data. Quite a few optimal sampling methods have been developed for parametric models in which the loss functions are differentiable with respect to parameters. However, they do not apply to quantile regression (QR) models as the involved check function is not differentiable. To circumvent the non-differentiability problem, we consider directly estimating the linear QR coefficient by minimizing the Hansen-Hurwitz estimator of the usual loss function for QR. We establish the asymptotic normality of the resulting estimator under a generic sampling method, and then develop optimal subsampling methods for linear QR. In particular, we propose a one-stage subsampling method, which depends only on the lengths of covariates, and a two-stage subsampling method, which is a combination of the one-stage sampling and the ideal optimal subsampling methods. Our simulation and real data based simulation studies show that the two recommended sampling methods always outperform simple random sampling in terms of mean square error, whether the linear QR model is valid or not. (c) 2020 Societe statistique du Canada

关键词： Big data Hansen– Hurwitz estimator linear quantile regression optimal subsampling uniform sampling

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Unveiling the drivers contributing to global wheat yield shocks through quantile regression

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Artificial Intelligence in Agriculture 2025年第3期15卷 564-572页

作者： Vishwakarma, Srishti Zhang, Xin Lyubchich, Vyacheslav Appalachian Laboratory University of Maryland Center for Environmental Science 301 Braddock Road FrostburgMD21532 United States Computational Sciences and Engineering Division Oak Ridge National Laboratory 1 Bethel Valley Road Oak RidgeTN37830 United States Chesapeake Biological Laboratory University of Maryland Center for Environmental Science 146 Williams Street SolomonsMD20688 United States

Sudden reductions in crop yield (i.e., yield shocks) severely disrupt the food supply, intensify food insecurity, depress farmers' welfare, and worsen a country's economic conditions. Here, we study the spatiotemporal patterns of wheat yield shocks, quantified by the lower quantiles of yield fluctuations, in 86 countries over 30 years. Furthermore, we assess the relationships between shocks and their key ecological and socioeconomic drivers using quantile regression based on statistical (linear quantile mixed model) and machine learning (quantile random forest) models. Using a panel dataset that captures spatiotemporal patterns of yield shocks and possible drivers in 86 countries, we find that the severity of yield shocks has been increasing globally since 1997. Moreover, our cross-validation exercise shows that quantile random forest outperforms the linear quantile regression model. Despite this performance difference, both models consistently reveal that the severity of shocks is associated with higher weather stress, nitrogen fertilizer application rate, and gross domestic product (GDP) per capita (a typical indicator for economic and technological advancement in a country). While the unexpected negative association between more severe wheat yield shocks and higher fertilizer application rate and GDP per capita does not imply a direct causal effect, they indicate that the advancement in wheat production has been primarily on achieving higher yields and less on lowering the possibility and magnitude of sharp yield reductions. Hence, in the context of growing extreme weather stress, there is a critical need to enhance the technology and management practices that mitigate yield shocks to improve the resilience of the world food systems. © 2025 The Authors

关键词： linear quantile regression Machine learning quantile random forest Wheat yield shock

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High-dimensional model averaging for quantile regression

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CANADIAN JOURNAL OF STATISTICS-REVUE CANADIENNE DE STATISTIQUE 2024年第2期52卷 618-635页

作者： Xie, Jinhan Ding, Xianwen Jiang, Bei Yan, Xiaodong Kong, Linglong Yunnan Univ Key Lab Stat Modeling & Data Anal Yunnan Prov Kunming 650091 Yunnan Peoples R China Univ Alberta Dept Math & Stat Sci Edmonton AB Canada Jiangsu Univ Technol Dept Stat Changzhou 213001 Jiangsu Peoples R China Shandong Univ Zhongtai Secur Inst Financial Studies Jinan Shandong Peoples R China

This article considers robust prediction issues in ultrahigh-dimensional (UHD) datasets and proposes combining quantile regression with sequential model averaging to arrive at a quantile sequential model averaging (QSMA) procedure. The QSMA method is made computationally feasible by employing a sequential screening process and a Bayesian information criterion (BIC) model averaging method for UHD quantile regression and provides a more accurate and stable prediction of the conditional quantile of a response variable. Meanwhile, the proposed method shows effective behaviour in dealing with prediction in UHD datasets and saves a great deal of computational cost with the help of the sequential technique. Under some suitable conditions, we show that the proposed QSMA method can mitigate overfitting and yields reliable predictions. Numerical studies, including extensive simulations and a real data example, are presented to confirm that the proposed method performs well.

关键词： Bayesian information criterion linear quantile regression model averaging quantile prediction error ultrahigh-dimensional data

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Applications of Probabilistic Forecasting in Demand Response

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APPLIED SCIENCES-BASEL 2024年第21期14卷 9716页

作者： Ruiz-Abellon, Maria Carmen Fernandez-Jimenez, Luis Alfredo Guillamon, Antonio Gabaldon, Antonio Tech Univ Cartagena Dept Appl Math & Stat Cartagena 30202 Spain Univ La Rioja Dept Elect Engn Logrono 26004 Spain Tech Univ Cartagena Power Syst Grp Cartagena 30202 Spain

Studies on probabilistic demand forecasting remain relatively limited compared with point forecasting, despite it being especially valuable for operational and planning purposes. This paper demonstrates different applications of probabilistic forecasting in demand response, together with Physical-Based Load Models. The first application shows how to determine the percentage of uncertainty potentially covered by demand response throughout a day, whereas the second application deals with obtaining the number of consumers that would be needed in demand response actions for a desired percentage of coverage. Finally, in the third application, a specific hourly strategy is proposed for demand response policies. These applications facilitate the aggregator's energy purchasing in the market and the planning of subsequent consumption adjustments through demand response to minimize deviations from the purchased energy. The approach is illustrated using hourly demand data from a small Spanish city, and two machine learning methods were used to produce a set of probabilistic forecasts and compare results: linear quantile regression and a quantile regression Forest. Main results show a significant reduction in deviations from the purchased energy after applying the proposed strategy, especially in the case of the forecasting method being less accurate (40.95% and 33.62% of reduction, respectively).

关键词： short-term load forecasting probabilistic forecasting linear quantile regression quantile regression forest demand response

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A bias-adjusted estimator in quantile regression for clustered data

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ECONOMETRICS AND STATISTICS 2022年 23卷 165-186页

作者： Battagliola, Maria Laura Sorensen, Helle Tolver, Anders Staicu, Ana-Maria Univ Copenhagen Dept Math Sci Univ Pk 5 DK-2100 Copenhagen Denmark North Carolina State Univ Dept Stat 2311 Stinson DrCampus Box 8203 Raleigh NC 27695 USA

quantile regression models with random effects are useful for studying associations between covariates and quantiles of the response distribution for clustered data. Parameter estimation is examined for a class of mixed-effects quantile regression models, with focus on settings with many but small clusters. The main contributions are the following: (i) documenting that existing methods may lead to severely biased estimators for fixed effects parameters;(ii) proposing a new two-step estimation methodology where predictions of the random effects are first computed by a pseudo likelihood approach (the LQMM method) and then used as offsets in standard quantile regression;(iii) proposing a novel bootstrap sampling procedure in order to reduce bias of the two-step estimator and compute confidence intervals. The proposed estimation and associated inference is assessed numerically through rigorous simulation studies and applied to an AIDS Clinical Trial Group (ACTG) study. (c) 2021 EcoSta Econometrics and Statistics. Published by Elsevier B.V. All rights reserved.

关键词： linear quantile regression Clustered data Random effects Bias-adjustment Wild bootstrap AIDS clinical trial group study

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Sectoral electricity consumption modeling with D-vine quantile regression: The US electricity market case

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ENERGY SOURCES PART B-ECONOMICS PLANNING AND POLICY 2023年第1期18卷 Article: 2160523页

作者： Evkaya, Ozan Yilmaz, Bilgi Haliloglu, Ebru Yuksel Univ Edinburgh Sch Math Edinburgh Scotland TU Kaiserslautern Math Dept Gottlieb Daimler Str Gebaude 48Raum 621 D-67663 Kaiserslautern Germany Gazi Univ Ind Engn Dept Ankara Turkiye

Efficient electricity demand planning is crucial for energy market actors. However, it is difficult as a consequence of climate change. We aim at investigating how climate variables (heating and cooling degree days) may affect electricity demand. By examining electricity consumption in various US sectors, we explore this relationship using parametric and non-parametric D-vine quantile regression models that exploits the dependence between covariates and allows sequential covariate selection. The results are compared against the classical linear quantile regression. We find a positive effect of the climatic variables on electricity consumption that is as heating and cooling degree days increase electricity demand rises in all sectors, and cooling need has a greater impact than heating need. Evidence suggests that residential and commercial electricity consumptions are affected the most, while industrial and transport sector consumptions are less sensitive. The D-vine quantile regression performs better than the linear quantile regression for almost all sectors.

关键词： Climate change cooling degree days (CDD) D-vine quantile regression electricity demand forecasting heating degree days (HDD) linear quantile regression

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Random projections for quantile ridge regression

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STAT 2021年第1期10卷

作者： Zhou, Yan Liang, Jiang Hu, Yaohua Lian, Heng Shenzhen Univ Coll Math & Stat Shenzhen 518060 Peoples R China City Univ Hong Kong Dept Math Kowloon Hong Kong Peoples R China

quantile regression estimate gives more complete information about the response distribution but is more costly to compute than mean regression. When the dimension is large, a ridge penalty is conventionally used to stabilize the estimate and achieve better bias-variance trade-off. We investigate a random projection approach to ease the computational burden and establish its statistical properties. Monte Carlo studies are carried out to illustrate the computational and statistical properties of the estimates.

关键词： dimension reduction linear quantile regression random projection ridge regression

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Simultaneous linear quantile regression: A Semiparametric Bayesian Approach

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BAYESIAN ANALYSIS 2012年第1期7卷 51-71页

作者： Tokdar, Surya T. Kadane, Joseph B. Duke Univ Dept Stat Sci Durham NC 27708 USA Carnegie Mellon Univ Dept Stat Pittsburgh PA 15213 USA

We introduce a semi-parametric Bayesian framework for a simultaneous analysis of linear quantile regression models. A simultaneous analysis is essential to attain the true potential of the quantile regression framework, but is computationally challenging due to the associated monotonicity constraint on the quantile curves. For a univariate covariate, we present a simpler equivalent characterization of the monotonicity constraint through an interpolation of two monotone curves. The resulting formulation leads to a tractable likelihood function and is embedded within a Bayesian framework where the two monotone curves are modeled via logistic transformations of a smooth Gaussian process. A multivariate extension is suggested by combining the full support univariate model with a linear projection of the predictors. The resulting single-index model remains easy to fit and provides substantial and measurable improvement over the first order linear heteroscedastic model. Two illustrative applications of the proposed method are provided.

关键词： Bayesian Inference Bayesian Nonparametric Models Gaussian Processes Joint quantile Model linear quantile regression Monotone Curves

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Joint Estimation of quantile Planes Over Arbitrary Predictor Spaces

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2017年第519期112卷 1107-1120页

作者： Yang, Yun Tokdar, Surya T. Duke Univ Stat Sci Box 90251 Durham NC 27708 USA

In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parameterization that characterizes any collection of noncrossing quantile planes over arbitrarily shaped convex predictor domains in any dimension by means of unconstrained scalar, vector and function valued parameters. Statistical models based on this parameterization inherit a fast computation of the likelihood function, enabling penalized likelihood or Bayesian approaches to model fitting. We introduce a complete Bayesian methodology by using Gaussian process prior distributions on the function valued parameters and develop a robust and efficient Markov chain Monte Carlo parameter estimation. The resulting method is shown to offer posterior consistency under mild tail and regularity conditions. We present several illustrative examples where the new method is compared against existing approaches and is found to offer better accuracy, coverage and model fit. Supplementary materials for this article are available online.

关键词： Bayesian inference Bayesian nonparametric models Gaussian processes Joint quantile model linear quantile regression

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Combining Conformal Prediction and Genetic Programming for Symbolic Interval regression 17

Combining Conformal Prediction and Genetic Programming for S...

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Genetic and Evolutionary Computation Conference (GECCO)

作者： Pham Thi Thuong Nguyen Xuan Hoai Yao, Xin Univ Informat & Commun Technol IT Dept Thainguyen Vietnam Hanoi Univ HANU IT R&D Ctr Hanoi Vietnam Southern Univ Sci & Technol Dept Comp Sci & Engn Shenzhen Peoples R China

ISBN: (纸本)9781450349208

Symbolic regression has been one of the main learning domains for Genetic Programming. However, most work so far on using genetic programming for symbolic regression only focus on point prediction. The problem of symbolic interval regression is for each input to find a prediction interval containing the output with a given statistical confidence. This problem is important for many risk-sensitive domains (such as in medical and financial applications). In this paper, we propose the combination of conformal prediction and genetic programming for solving the problem of symbolic interval regression. We study two approaches called black-box conformal prediction genetic programming (black-box CPGP) and white-box conformal prediction genetic programming (white-box CPGP) on a number of benchmarks and previously used problems. We compare the performance of these approaches with two popular interval regressors in statistic and machine learning domains, namely, the linear quantile regression and quantile random forrest. The experimental results show that, on the two performance metrics, black-box CPGP is comparable to the linear quantile regression and not much worse than the quantile random forrest on validity and much better than them on efficiency.

关键词： Genetic Programming quantile regression linear quantile regression quantile regression Forests Conformal Prediction Interval Prediction Symbolic regression

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