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nonparametric quantile regression with missing data using local estimating equations

JOURNAL OF nonparametric STATISTICS 2022年第1期34卷 164-186页

作者： Wang, Chunyu Tian, Maozai Tang, Man-Lai Renmin Univ China Ctr Appl Stat Sch Stat Beijing Peoples R China Xinjiang Med Univ Dept Med Engn & Technol Urumqi Peoples R China Lanzhou Univ Finance & Econ Sch Stat Lanzhou Peoples R China Xinjiang Univ Finance Sch Stat & Informat Urumqi Peoples R China Brunel Univ London Coll Engn Design Phys Sci Dept Math Uxbridge Middx England Hang Seng Univ Hong Kong Dept Math Stat & Insurance Siu Lek Yuen Hong Kong Peoples R China

In this paper, we propose augmented inverse probability weighted (AIPW) local estimating equations in dealing with missing data in nonparametric quantile regression context. The missing mechanism here is missing at random. To avoid the problem of misspecification, we adopt nonparametric approach to estimate the propensity score and conditional expectations of estimating functions. The asymptotic properties of our proposed estimator are studied. Majorisation-minimisation algorithm is used to circumvent the nonsmoothness of check function at the origin. When it comes to the choice of bandwidth, the theoretical expression of local optimal bandwidth is derived based on asymptotic properties. Moreover, we apply smoothed bootstrap method to obtain the empirical mean square error and use cross-validation to determine the bandwidth in practice. Simulations are conducted to compare the performance of our proposed methods with other existing methods. Finally, we illustrate our methodology with an analysis of non-insulin-dependent diabetes mellitus data set.

关键词： Missing data augmented inverse probability weighted method local estimating equations nonparametric quantile regression

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Variable selection for nonparametric quantile regression via measurement error model

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STATISTICAL PAPERS 2022年第6期64卷 2207-2224页

作者： Lai, Peng Yan, Xi Sun, Xin Pang, Haozhe Zhou, Yanqiu Nanjing Univ Informat Sci & Technol Sch Math & Stat Nanjing 210044 Peoples R China Guangxi Univ Sci & Technol Sch Sci Liuzhou 545006 Peoples R China

This paper proposes a variable selection procedure for the nonparametric quantile regression based on the measurement error model (MEM). The "false" Gaussian measurement error is forced into the covariates to construct a nonparametric quantile regression loss function with the MEM framework. Under this MEM framework, the variable selection procedure is completed, and the asymptotic normality of the estimates and the consistency of variable selection are verified. Some Monte Carlo simulations and a real data application are conducted to evaluate the performance of the proposed procedure.

关键词： Variable selection nonparametric quantile regression Measurement error model Gaussian product kernel

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Approximate nonparametric quantile regression in reproducing kernel Hilbert spaces via random projection

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INFORMATION SCIENCES 2021年 547卷 244-254页

作者： Zhang, Fode Li, Rui Lian, Heng Southwestern Univ Finance & Econ Sch Stat Ctr Stat Res Chengdu 611130 Peoples R China Shanghai Univ Int Business & Econ Sch Stat & Informat Shanghai Peoples R China City Univ Hong Kong Dept Math Hong Kong Peoples R China City Univ Hong Kong Shenzhen Res Inst Shenzhen Peoples R China

nonparametric quantile regression is a commonly used nonlinear quantile model. One general and popular approach is based on the use of kernels within a reproducing kernel Hilbert space (RKHS) framework, with the smoothing splines estimation as a special case. However, when the sample size n is large, the computational burden is heavy. Motivated by the recent advances in random projection for kernel nonparametric (mean) ridge regression (KRR), we consider an m-dimensional random projection approach for kernel quantile regression (KQR) with m << n. We establish a theoretical result showing that the sketched KQR still achieves the minimax convergence rate when m is at least as large as the effective statistical dimension of the problem. Some Monte Carlo studies are carried out for illustration purposes. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Dimension reduction Kernel method nonparametric quantile regression Random projection

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An Algorithm of nonparametric quantile regression

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JOURNAL OF STATISTICAL THEORY AND PRACTICE 2023年第2期17卷 32-32页

作者： Huang, Mei Ling Han, Yansan Marshall, William Brock Univ Dept Math & Stat St Catharines ON L2S 3A1 Canada

Extreme events, such as earthquakes, tsunamis, and market crashes, can have substantial impact on social and ecological systems. quantile regression can be used for predicting these extreme events, making it an important problem that has applications in many fields. Estimating high conditional quantiles is a difficult problem. Regular linear quantile regression uses an L-1 loss function [Koenker in quantile regression, Cambridge University Press, Cambridge, 2005], and the optimal solution of linear programming for estimating coefficients of regression. A problem with linear quantile regression is that the estimated curves for different quantiles can cross, a result that is logically inconsistent. To overcome the curves crossing problem, and to improve high quantile estimation in the nonlinear case, this paper proposes a nonparametric quantile regression method to estimate high conditional quantiles. A three-step computational algorithm is given, and the asymptotic properties of the proposed estimator are derived. Monte Carlo simulations show that the proposed method is more efficient than linear quantile regression method. Furthermore, this paper investigates COVID-19 and blood pressure real-world examples of extreme events by using the proposed method.

关键词： Conditional quantile Extreme value distribution Generalized Pareto distribution Kernel estimation Linear programming nonparametric quantile regression

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Investigating distribution of nitrate concentration using ensemble nonparametric quantile regression

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SCIENCE OF THE TOTAL ENVIRONMENT 2021年 777卷 146098-146098页

作者： Shin, Joonho You, Hojun Kaown, Dugin Koh, Eun-Hee Lee, Sanghoon Lim, Chae Young Lee, Kang-Kun Seoul Natl Univ Dept Stat Kwanak Ro 1 Seoul 08826 South Korea Seoul Natl Univ Sch Earth & Environm Sci Kwanak Ro 1 Seoul 08826 South Korea

Nitrate (NO3-) pollution in groundwater is a major concern due to its negative health effects;therefore, accurately estimating and predicting the NO3- concentration in groundwater is necessary. The NO3- concentration distribution can be used to find less polluted areas, and these identified areas can be candidates for drinking water resources. We considered a total of 14,297 NO3- concentration observations in South Korea. Altitude, slope, land use, hydrogeological unit, and surface soil texture data were also collected to assess the covariates that affect NO3- concentration levels. Sample quantiles display nonlinear patterns based on these covariates. Thus, we propose using an ensemble nonparametric quantile regression approach to determine the NO3- concentration distribution. The proposed approach is a data-driven method that ensembles nonlinear quantile models to capture the complex relationships between quantiles of the response variable and the covariates while controlling the computational complexity, which are advantages over non-ensemble quantile regression methods. The validation study demonstrates that the proposed method exhibits a smaller loss value compared to that of the non-ensemble models considered for comparison. We investigated lower quantile maps of NO3- concentration (5% and 10%), as we are interested in less polluted areas. The proposed model attempts to reach the sample quantile values while a non-ensemble nonlinear model with altitude and slope does not except land use is coniferous at low altitude. We created a proportional map with less polluted areas at the district level using the proposed approach. This provided us with the top five districts (Samcheok City, Geochang County, Yanggu County, Inje County, and Yeongwol County) with the highest proportions of less-polluted areas in South Korea. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Groundwater nitrate analysis nonparametric quantile regression Ensemble method Spatial distribution Water resource management

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Convergence rate for nonparametric quantile regression with a total variation penalty

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STAT 2021年第1期10卷

作者： Liu, Jiamin Xu, Wangli Lian, Heng Renmin Univ China Sch Stat Beijing Peoples R China City Univ Hong Kong Dept Math Hong Kong Peoples R China

quantile regression with a total variation penalty was previously proposed due to its computational expediency as well as its local adaptiveness. However, the convergence rate of the method in this setting has been not rigorously established. In this short communication, we establish the convergence rate of O-p(n(-1/3)) for the penalized estimator which is the same as in penalized least squares regression. Different from penalized least squares regression, in order to deal with the quantile loss function, we heavily rely on the Rademacher complexity of the class of functions of bounded variation.

关键词： minimax rate nonparametric quantile regression total variation penalty

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Longitudinal Study of the Positive Academic Emotion Effects on Children's Mathematics and Science Achievements-Using nonparametric quantile regression

Longitudinal Study of the Positive Academic Emotion Effects ...

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作者： Yu Wang Lingyu Kong Dianjun Lu School of Mathematics and Statistics of Qinghai Normal University

This article attempts to address the interesting and important research topic and to give an in-depth longitudinal study of Xining high school students using a so called "double-kernel" nonparametric quantile regression approach. The conclusion is that the process-science-push's and process-math-push's points is 4, the result-science-push's point is 3, etc. All the findings are useful for parents understand students' learning status, especially for educators make educational plans.

关键词： quantile regression academic emotion mathematics and science achievements nonparametric quantile regression double-kernel approach

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nonparametric screening for additive quantile regression in ultra-high dimension

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JOURNAL OF nonparametric STATISTICS 2025年第1期37卷 148-168页

作者： Li, Daoji Kong, Yinfei Zerom, Dawit Calif State Univ Coll Business & Econ Fullerton CA 92831 USA

In practical applications, one often does not know the 'true' structure of the underlying conditional quantile function, especially in the ultra-high dimensional setting. To deal with ultra-high dimensionality, quantile-adaptive marginal nonparametric screening methods have been recently developed. However, these approaches may miss important covariates that are marginally independent of the response, or may select unimportant covariates due to their high correlations with important covariates. To mitigate such shortcomings, we develop a conditional nonparametric quantile screening procedure (complemented by subsequent selection) for nonparametric additive quantile regression models. Under some mild conditions, we show that the proposed screening method can identify all relevant covariates in a small number of steps with probability approaching one. The subsequent narrowed best subset (via a modified Bayesian information criterion) also contains all the relevant covariates with overwhelming probability. The advantages of our proposed procedure are demonstrated through simulation studies and a real data example.

关键词： Additive model feature screening high dimension nonparametric quantile regression sure screening property variable selection

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quantile regression under Truncated,Censored and Dependent Assumptions

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Acta Mathematicae Applicatae Sinica 2025年第2期41卷 479-497页

作者： Chang-sheng LIU Yun-jiao LU Si-li NIU School of Mathematics and Physics Henan University of Urban ConstructionPingdingshan 467036China School of Mathematical Sciences Tongji UniversityShanghai 200092China

In this paper,we focus on the problem of nonparametric quantile regression with left-truncated and right-censored *** on Nadaraya-Watson(NW)Kernel smoother and the technique of local linear(LL)smoother,we construct the NW and LL estimators of the conditional *** strong mixing assumptions,we establish asymptotic representation and asymptotic normality of the *** sample behavior of the estimators is investigated via simulation,and a real data example is used to illustrate the application of the proposed methods.

关键词： asymptotic normality asymptotic representation nonparametric quantile regression truncated and censored -mixing

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Toward enhancing environmental quality in OECD countries: Role of municipal waste, renewable energy, environmental innovation, and environmental policy

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RENEWABLE ENERGY 2023年第1期211卷 975-984页

作者： Su, Mengying Yang, Zhongyu Abbas, Shujaat Bilan, Yuriy Majewska, Agnieszka Guangxi Minzu Univ Coll Econ Nanning 530006 Peoples R China Lanzhou Univ Sch Math & Stat Lanzhou 730000 Peoples R China Ural Fed Univ Grad Sch Econ & Management Ekaterinburg Russia Czech Univ Life Sci Prague Fac Econ & Management Kamycka 129 Prague 16500 Czech Republic Univ Szczecin Inst Econ & Finance Ul A Mickiewicza 64 PL-71101 Szczecin Poland

The considerable increase in municipal waste has become a primary global concern due to the contamination of the environment through the emission of greenhouse gases. Therefore, many OECD countries have adopted municipal waste management practices. This study is a baseline attempt to explore the long-term effect of municipal waste management along with the energy transition, environmental innovation, and environmental policy stringency on GHG emissions in ten OECD countries from 1994 to 2020. This objective is realized by using non-parametric panel quantile regression. The estimated result reveals the asymmetric effect of selected explanatory variables on GHG emissions at various quantiles. The findings show that an increase in municipal waste can increase GHGs emissions at lower quantiles, while an insignificant effect is observed at higher quantiles. Similarly, energy transition, environmental innovation, and environmental policy stringency reveal asymmetric effects across the quantiles. The findings urge OECD countries to adopt more efficient municipal waste management practices and encourage renewable energy transition and environmental innovation. Envi-ronmental policy stringency can also be instrumental in enhancing environmental sustainability.

关键词： Greenhouse gas emissions Municipal waste Green energy Environmental innovation Environmental policy nonparametric quantile regression

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