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Generative quantile regression with Variability Penalty

JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 2024年第4期33卷 1202-1213页

作者： Wang, Shijie Shin, Minsuk Bai, Ray Univ South Carolina Dept Stat Columbia SC 29208 USA Gauss Labs Palo Alto CA USA

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://***/shijiew97/PGQR.

关键词： Conditional quantile Deep generative model Generative learning Joint quantile model Neural networks nonparametric quantile regression

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Comparing time varying regression quantiles under shift invariance

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BERNOULLI 2023年第2期29卷 1527-1554页

作者： Dhar, Subhra Sankar Wu, Weichi IIT Kanpur Dept Math & Stat Kanpur 208016 India Tsinghua Univ Ctr Stat Sci Dept Ind Engn Beijing 100084 Peoples R China

This article investigates whether time-varying quantile regression curves are the same up to the horizontal shift or not. The errors and the covariates involved in the regression model are allowed to be locally stationary. We formalize this issue in a corresponding non-parametric hypothesis testing problem, and develop an integrated -squared-norm based test (SIT) as well as a simultaneous confidence band (SCB) approach. The asymptotic prop-erties of SIT and SCB under null and local alternatives are derived. Moreover, the asymptotic properties of these tests are also studied when the compared data sets are dependent. We then propose valid wild bootstrap algorithms to implement SIT and SCB. Furthermore, the usefulness of the proposed methodology is illustrated via analysing simulated and real data related to COVID-19 outbreak.

关键词： Bootstrap comparison of curves confidence band hypothesis testing locally stationary process nonparametric quantile regression COVID-19

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Element-wise estimation error of generalized Fused Lasso

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BERNOULLI 2023年第4期29卷 2691-2718页

作者： Zhang, Teng Chatterjee, Sabyasachi Univ Cent Florida Dept Math Orlando FL 32816 USA Univ Illinois Dept Stat Urbana IL 61820 USA

The main result of this article is that we obtain an elementwise error bound for the Fused Lasso estimator for any general convex loss function rho. We then focus on the special cases when either rho is the square loss function (for mean regression) or is the quantile loss function (for quantile regression) for which we derive new pointwise error bounds. Even though error bounds for the usual Fused Lasso estimator and its quantile version have been studied before;our bound appears to be new. This is because all previous works bound a global loss function like the sum of squared error, or a sum of huber losses in the case of quantile regression in Padilla and Chatterjee (Biometrika 109 (2022) 751-768). Clearly, element wise bounds are stronger than global loss error bounds as it reveals how the loss behaves locally at each point. Our element wise error bound also has a clean and explicit dependence on the tuning parameter lambda which informs the user of a good choice of lambda. In addition, our bound is nonasymptotic with explicit constants and is able to recover almost all the known results for Fused Lasso (both mean and quantile regression) with additional improvements in some cases.

关键词： Adaptive risk bounds generalized Fused Lasso law of iterated logarithm nonasymptotic risk bounds nonparametric quantile regression pointwise risk bounds total variation denoising

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Nonperforming loan of European Islamic banks over the economic cycle

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ANNALS OF OPERATIONS RESEARCH 2022年第2期313卷 773-808页

作者： Ben Bouheni, Faten Obeid, Hassan Margarint, Elena Ipag Business Sch Finance Dept Paris France European Business Sch Paris INSEEC U Res Ctr Paris France Natl Bank Moldova Kishinev Moldova

This paper investigates the variation in nonperforming loans over the economic cycle and the effect of past returns based on a nonparametric quantile analysis of the largest Islamic banks in the United Kingdom and Turkey from 2010 to 2019. The findings show a weak variation in nonperforming loans that increases with an increasing return on assets and a decreasing return on equity and decreases in an inverse scenario. As a result, the credit risk of Islamic banks is countercyclical. We suggest that the inverse relationships evidence the existence of trade-offs within bank returns and credit risk. Thus, banks' past profitability and risk mitigation are determinants of asset quality. These findings provide support for risk-taking and risk-sharing principles in which flight-to-safety mirrors the calibration of risk factors in a disruptive economy. Our estimates indicate that nonparametric quantile regression captures considerably more variation in a risk-return analysis.

关键词： Nonperforming loans Returns Economic cycle nonparametric quantile regression European Islamic banks

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Climate change and urban total factor productivity: evidence from capital cities and municipalities in China

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EMPIRICAL ECONOMICS 2023年第1期65卷 401-441页

作者： Chen, Li Jiang, Bin Wang, Chuan Xiamen Univ Wang Yanan Inst Studies Econ Xiamen Peoples R China Zhongnan Univ Econ & Law Wenlan Sch Business Wuhan Peoples R China Xiamen Univ Sch Econ Xiamen Peoples R China Xiamen Univ MOE Key Lab Econometr Xiamen Peoples R China

This paper studies climate change impacts on total factor productivity (TFP) in China using economic and climatic data for provincial capital cities and municipalities from 1998 to 2017. We employ a novel nonparametric quantile method to decompose historical temperature data into multiple temperature quantiles, which are then used in our regression analysis to avoid estimation bias caused by seasonal heterogeneity of temperatures across China. Specifically, we create three temperature quantiles for each city to represent their extremely high temperatures in summer, extremely low temperatures in winter, and mild temperatures in spring and fall. In general, we find that a warming climate has a significant negative impact on TFP in the long-run, while in the short term, only increases in extreme temperatures exert significant negative effects on TFP growth. However, the temperature effects on TFP vary substantially across coastal capital cities, inland capital cities, and municipalities due to their differences in geography, development levels, and political positions. Finally, our results are robust when spatial spillover, temporal lagging, and labor intensity effects are taken into account.

关键词： Climate change Total factor productivity nonparametric quantile regression

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Fast and locally adaptive Bayesian quantile smoothing using calibrated variational approximations

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STATISTICS AND COMPUTING 2024年第1期34卷 15-15页

作者： Onizuka, Takahiro Hashimoto, Shintaro Sugasawa, Shonosuke Hiroshima Univ Dept Math 1-7-1 Kagamiyama Higashihiroshima Hiroshima 7398521 Japan Keio Univ Fac Econ 2-15-45 Mita Minato Tokyo 1088345 Japan

quantiles are useful characteristics of random variables that can provide substantial information on distributions compared with commonly used summary statistics such as means. In this study, we propose a Bayesian quantile trend filtering method to estimate the non-stationary trend of quantiles. We introduce general shrinkage priors to induce locally adaptive Bayesian inference on trends and mixture representation of the asymmetric Laplace likelihood. To quickly compute the posterior distribution, we develop calibrated mean-field variational approximations to guarantee that the frequentist coverage of credible intervals obtained from the approximated posterior is a specified nominal level. Simulation and empirical studies show that the proposed algorithm is computationally much more efficient than the Gibbs sampler and tends to provide stable inference results, especially for high/low quantiles.

关键词： Calibration Shrinkage prior Trend filtering Variational Bayes nonparametric quantile regression Model misspecification

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On the Impact of Climate Change Policies on the Clean Technology Innovation: Evidence from Patent Data Analysis

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ENVIRONMENTAL AND CLIMATE TECHNOLOGIES 2023年第1期27卷 850-863页

作者： Balcilar, Mehmet Agan, Busra Univ New Haven Dept Econ & Business Analyt 300 Boston Post Rd West Haven CT 06516 USA OSTIM Tech Univ Dept Econ Ankara Turkiye

This study investigates the role of environmental policies and regulations in mitigating climate change by promoting clean innovations and discouraging dirty ones. Utilizing nonparametric copula and quantile estimation techniques, along with carefully constructed innovation variables based on patents from 2000 to 2021 across 34 countries, the research examines the effects of policy interventions and external events on energy-related innovations. Findings reveal that climate policy interventions effectively promote clean innovation, particularly at higher levels, and discourage dirty innovations. Therefore, climate change policies and regulations are crucial in achieving net-zero carbon emission targets.

关键词： Clean and dirty innovation climate change climate change mitigation policies copula environmental policy nonparametric dependence test nonparametric quantile regression sustainable development

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Predicting extreme value at risk: nonparametric quantile regression with refinements from extreme value theory

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2012年第12期56卷 4081-4096页

作者： Schaumburg, Julia Univ Berlin Sch Business & Econ Inst Stat & Econometr Chair Econometr D-10178 Berlin Germany

A framework is introduced allowing us to apply nonparametric quantile regression to Value at Risk (VaR) prediction at any probability level of interest. A monotonized double kernel local linear estimator is used to estimate moderate (1%) conditional quantiles of index return distributions. For extreme (0.1%) quantiles, nonparametric quantile regression is combined with extreme value theory. The abilities of the proposed estimators to capture market risk are investigated in a VaR prediction study with empirical and simulated data. Possibly due to its flexibility, the out-of-sample forecasting performance of the new model turns out to be superior to competing models. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Value at risk nonparametric quantile regression Risk management Extreme value statistical applications Monotonization

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BASELINE DRIFT ESTIMATION FOR AIR QUALITY DATA USING quantile TREND FILTERING

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ANNALS OF APPLIED STATISTICS 2020年第2期14卷 585-604页

作者： Brantley, Halley L. Guinness, Joseph Chi, Eric C. North Carolina State Univ Dept Stat Raleigh NC 27695 USA Cornell Univ Dept Stat & Data Sci Ithaca NY 14853 USA

We address the problem of estimating smoothly varying baseline trends in time series data. This problem arises in a wide range of fields, including chemistry, macroeconomics and medicine;however, our study is motivated by the analysis of data from low cost air quality sensors. Our methods extend the quantile trend filtering framework to enable the estimation of multiple quantile trends simultaneously while ensuring that the quantiles do not cross. To handle the computational challenge posed by very long time series, we propose a parallelizable alternating direction method of multipliers (ADMM) algorithm. The ADMM algorthim enables the estimation of trends in a piecewise manner, both reducing the computation time and extending the limits of the method to larger data sizes. We also address smoothing parameter selection and propose a modified criterion based on the extended Bayesian information criterion. Through simulation studies and our motivating application to low cost air quality sensor data, we demonstrate that our model provides better quantile trend estimates than existing methods and improves signal classification of low-cost air quality sensor output.

关键词： Air quality nonparametric quantile regression trend estimation

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Non-separable models with high-dimensional data

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JOURNAL OF ECONOMETRICS 2019年第2期212卷 646-677页

作者： Su, Liangjun Ura, Takuya Zhang, Yichong Singapore Management Univ Sch Econ 90 Stamford Rd Singapore 178903 Singapore Univ Calif Davis Dept Econ One Shields Ave Davis CA 95616 USA

This paper studies non-separable models with a continuous treatment when the dimension of the control variables is high and potentially larger than the effective sample size. We propose a three-step estimation procedure to estimate the average, quantile, and marginal treatment effects. In the first stage we estimate the conditional mean, distribution, and density objects by penalized local least squares, penalized local maximum likelihood estimation, and numerical differentiation, respectively, where control variables are selected via a localized method of L-1-penalization at each value of the continuous treatment. In the second stage we estimate the average and marginal distribution of the potential outcome via the plug-in principle. In the third stage, we estimate the quantile and marginal treatment effects by inverting the estimated distribution function and using the local linear regression, respectively. We study the asymptotic properties of these estimators and propose a weighted-bootstrap method for inference. Using simulated and real datasets, we demonstrate that the proposed estimators perform well in finite samples. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Average treatment effect High dimension Least absolute shrinkage and selection operator (Lasso) nonparametric quantile regression Nonseparable models quantile treatment effect Unconditional average structural derivative

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