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Simultaneous fitting of Bayesian penalised quantile splines

COMPUTATIONAL STATISTICS & DATA ANALYSIS 2019年 134卷 93-109页

作者： Rodrigues, T. Dortet-Bernadet, J. -L. Fan, Y. Univ New South Wales Sch Math & Stat Sydney NSW 2052 Australia Univ Brasilia Dept Estat BR-70910900 Brasilia DF Brazil Univ Strasbourg CIIRS UMR 7501 Inst Rech Math Avancee Strasbourg France

Bayesian simultaneous estimation of nonparametric quantile curves is a challenging problem, requiring a flexible and robust data model whilst satisfying the monotonicity or noncrossing constraints on the quantiles. The pyramid quantile regression method for simultaneous linear quantile fitting is adapted for the spline regression setting. In high dimensional problems, the choice of the pyramid locations becomes crucial for a robust parameter estimation. The optimal pyramid locations are derived which then allows for an efficient adaptive block-update MCMC scheme to be proposed for posterior computation. Simulation studies show that the proposed method provides estimates with significantly smaller errors and better empirical coverage probability when compared to existing alternative approaches. The method is illustrated with three real applications. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Bayesian quantile pyramid Simultaneous quantile regression B-splines O'Sullivan penalised splines nonparametric quantile regression

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nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates

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JOURNAL OF ECONOMETRICS 2019年第2期212卷 433-450页

作者： Chen, Xirong Li, Degui Li, Qi Li, Zheng Univ Int Business & Econ Sch Int Trade & Econ Beijing Peoples R China Univ York Dept Math York N Yorkshire England Texas A&M Univ Dept Econ College Stn TX 77843 USA NC State Univ Dept Agr & Resource Econ Raleigh NC 27606 USA

Allowing for the existence of irrelevant covariates, we study the problem of estimating a conditional quantile function nonparametrically with mixed discrete and continuous data. We estimate the conditional quantile regression function using the check-function based kernel method and suggest a data-driven cross-validation (CV) approach to simultaneously determine the optimal smoothing parameters and remove the irrelevant covariates. When the number of covariates is large, we first use a screening method to remove the irrelevant covariates and then apply the CV criterion to those that survive the screening procedure. Simulations and an empirical application demonstrate the usefulness of the proposed methods. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Cross-validation Discrete regressors Irrelevant covariates nonparametric quantile regression Screening

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A comparison of E. coli concentration estimates quantified by the EPA and a Michigan laboratory network using EPA Draft Method C

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JOURNAL OF MICROBIOLOGICAL METHODS 2020年 179卷 106086-106086页

作者： Lane, Molly J. Rediske, Richard R. McNair, James N. Briggs, Shannon Rhodes, Geoff Dreelin, Erin Sivy, Tami Flood, Matthew Scull, Brian Szlag, David Southwell, Benjamin Isaacs, Natasha M. Pike, Schuyler Grand Valley State Univ Annis Water Resources Inst 1 Campus Dr Allendale MI 49401 USA Michigan Dept Environm Great Lakes & Energy EGLE 525 W Allegan St Lansing MI 48909 USA Michigan State Univ Dept Fisheries & Wildlife Nat Resource Bldg420 Wilson RdRoom 13 E Lansing MI 48824 USA Saginaw Valley State Univ Dept Chem 7400 Bay Rd University Ctr MI 48710 USA Oakland Univ Dept Chem 146 Lib Dr Rochester MI 48309 USA Lake Super State Univ 650 W Easterday Ave Sault Ste Marie MI 49783 USA US Geol Survey USGS Upper Midwest Water Sci Ctr 5840 Enterprise Dr Lansing MI 48911 USA Ferris State Univ Shimadzu Core Lab Acad & Res Excellence 820 Campus Dr Big Rapids MI 49307 USA

We evaluated data from 10 laboratories that analyzed water samples from 82 recreational water sites across the state of Michigan between 2016 and 2018. Water sample replicates were analyzed by experienced U.S. Environmental Protection Agency (EPA) analysts and Michigan laboratories personnel, many of whom were newly trained, using EPA Draft Method C-a rapid quantitative polymerase chain reaction (qPCR) technique that provides same day Escherichia coli (E. coli) concentration results. Beach management decisions (i.e. remain open or issue an advisory or closure) based on E. coli concentration estimates obtained by Michigan labs and by the EPA were compared;the beach management decision agreed in 94% of the samples analyzed. We used the Wilcoxon one-sample signed rank test and nonparametric quantile regression to assess (1) the degree of agreement between E. coli concentrations quantified by Michigan labs versus the EPA and (2) Michigan lab E. coli measurement precision, relative to EPA results, in different years and water body types. The median quantile regression curve for Michigan labs versus EPA approximated the 1:1 line of perfect agreement more closely as years progressed. Similarly, Michigan lab E. coli estimates precision also demonstrated yearly improvements. No meaningful difference was observed in the degree of association between Michigan lab and EPA E. coli concentration estimates for inland lake and Great Lakes samples (median regression curve average slopes 0.93 and 0.95, respectively). Overall, our study shows that properly trained laboratory personnel can perform Draft Method C to a degree comparable with experienced EPA analysts. This allows health departments that oversee recreational water quality monitoring to be confident in qPCR results generated by the local laboratories responsible for analyzing the water samples.

关键词： E. coli nonparametric quantile regression qPCR Recreational water quality standard

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Does uncertainty move the gold price? New evidence from a nonparametric causality-in-quantiles test

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RESOURCES POLICY 2016年第0期49卷 74-80页

作者： Balcilar, Mehmet Gupta, Rangan Pierdzioch, Christian Eastern Mediterranean Univ Dept Econ Via Mersin 10 Famagusta Northern Cyprus Turkey Univ Pretoria Dept Econ ZA-0002 Pretoria South Africa Helmut Schmidt Univ Dept Econ Holstenhofweg 85POB 700822 D-22008 Hamburg Germany IPAG Business Sch Paris France

Much significant research has been done to study the links between gold returns and the returns of other asset classes in times of economic crisis and high uncertainty. We contribute to this research by using a novel nonparametric causality-in-quantiles test to study how measures of policy and equity-market uncertainty affect gold-price returns and volatility. For daily and monthly data, we find evidence of causality running from various uncertainty measures to both gold returns and volatility. For quarterly data, evidence of causality weakens and is significant only for some uncertainty measures and only for gold volatility. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Gold returns Gold volatility Causality nonparametric quantile regression Uncertainty

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nonparametric quantile regression Analysis on The Price-Volume Relationship of China Stock Market

Nonparametric Quantile Regression Analysis on The Price-Volu...

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2010 2nd IEEE International Conference on Information Management and Engineering(2010年IEEE第二届信息管理与工程国际会议 IEEE ICIME 2010)

作者： Chuanrui Fu School of Management Fuzhou University Fuzhou P.R. China

This paper adopts nonparametric quantile regression approach to empirically analyze the relationship between daily return and trading volume and the relationship between absolute return and trading volume in China stock market. The results show that both the relationship between return per se and volume and that between absolute return and volume are nonlinear. Secondly, when the trading volume is larger than a certain value, the relationship between return per se and volume is positive at the high quantile of return and negative at the low quantile of return. However, both the positive and negative relations get stronger with larger trading volume. Thirdly, the relationship between return and volume is asymmetric. Finally, the relationship between absolute return and trading volume is positive and stronger when the quantile of absolute return increases.

关键词： price-volume relationship nonparametric quantile regression smoothing splines nonlinear

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nonparametric estimation and inference on conditional quantile processes

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JOURNAL OF ECONOMETRICS 2015年第1期185卷 1-19页

作者： Qu, Zhongjun Yoon, Jungmo Boston Univ Dept Econ Boston MA 02215 USA Claremont Mckenna Coll Robert Day Sch Econ & Finance Claremont CA 91711 USA

This paper presents estimation methods and asymptotic theory for the analysis of a nonparametrically specified conditional quantile process. Two estimators based on local linear regressions are proposed. The first estimator applies simple inequality constraints while the second uses rearrangement to maintain quantile monotonicity. The bandwidth parameter is allowed to vary across quantiles to adapt to data sparsity. For inference, the paper first establishes a uniform Bahadur representation and then shows that the two estimators converge weakly to the same limiting Gaussian process. As an empirical illustration, the paper considers a dataset from Project STAR and delivers two new findings. (C) 2014 Elsevier B.V. All rights reserved.

关键词： nonparametric quantile regression Uniform Bahadur representation Uniform inference Treatment effect

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Stock holdings over the life cycle: Who hesitates to join the market?

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ECONOMIC SYSTEMS 2015年第3期39卷 423-438页

作者： Zhang, Linwan Wu, Weixing Wei, Ying Pan, Rulu Univ Int Business & Econ Sch Banking & Finance Beijing 100029 Peoples R China Columbia Univ Mailman Sch Publ Hlth New York NY 10032 USA Univ Queensland UQ Business Sch Brisbane Qld 4072 Australia

In this paper, we study the empirical relationship between age and individual wealth held in stocks, focusing on the heterogeneity of risk-taking over the life cycle in the population. We use micro-data and nonparametric quantile regression to argue that there is a pronounced life cycle pattern of risk-taking for households, which is conditional upon ownership. Specifically, we show that the fraction of stock investment decreases to bottom significantly in midlife and increases afterwards, contradicting the popular evidence claiming a hump-shaped pattern. The pressure of large financial obligations during middle age may be the reason for the crowding out of stock market risk-taking and could induce low capital returns for households. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Life cycle Stock market participation Targeting nonparametric quantile regression Raking

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Model Selection via Bayesian Information Criterion for quantile regression Models

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2014年第505期109卷 216-229页

作者： Lee, Eun Ryung Noh, Hohsuk Park, Byeong U. Univ Mannheim Dept Econ D-68131 Mannheim Germany Sookmyung Womens Univ Dept Stat Seoul 140742 South Korea Seoul Natl Univ Dept Stat Seoul 151747 South Korea

Bayesian information criterion (BIC) is known to identify the true model consistently as long as the predictor dimension is finite. Recently, its moderate modifications have been shown to be consistent in model selection even when the number of variables diverges. Those works have been done mostly in mean regression, but rarely in quantile regression. The best-known results about BIC for quantile regression are for linear models with a fixed number of variables. In this article, we investigate how BIC can be adapted to high-dimensional linear quantile regression and show that a modified BIC is consistent in model selection when the number of variables diverges as the sample size increases. We also discuss how it can be used for choosing the regularization parameters of penalized approaches that are designed to conduct variable selection and shrinkage estimation simultaneously. Moreover, we extend the results to structured nonparametric quantile models with a diverging number of covariates. We illustrate our theoretical results via some simulated examples and a real data analysis on human eye disease. Supplementary materials for this article are available online.

关键词： High dimension Linear quantile regression Model selection consistency nonparametric quantile regression Regularization parameter selection Shrinkage method

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Component selection in additive quantile regression models

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JOURNAL OF THE KOREAN STATISTICAL SOCIETY 2014年第3期43卷 439-452页

作者： Noh, Hohsuk Lee, Eun Ryung Catholic Univ Louvain Inst Stat Biostat & Sci Actuarielles ISBA Louvain Belgium Univ Mannheim Mannheim Germany

nonparametric additive models are powerful techniques for multivariate data analysis. Although many procedures have been developed for estimating additive components both in mean regression and quantile regression, the problem of selecting relevant components has not been addressed much especially in quantile regression. We present a doubly-penalized estimation procedure for component selection in additive quantile regression models that combines basis function approximation with a ridge-type penalty and a variant of the smoothly clipped absolute deviation penalty. We show that the proposed estimator identifies relevant and irrelevant components consistently and achieves the nonparametric optimal rate of convergence for the relevant components. We also provide an accurate and efficient computation algorithm to implement the estimator and demonstrate its performance through simulation studies. Finally, we illustrate our method via a real data example to identify important body measurements to predict percentage of body fat of an individual. (C) 2014 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

关键词： Additive model Covariate selection nonparametric quantile regression Second order cone programming Penalized estimation

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Significance testing in quantile regression

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ELECTRONIC JOURNAL OF STATISTICS 2013年第none期7卷 105-145页

作者： Volgushev, Stanislav Birke, Melanie Dette, Holger Neumeyer, Natalie Ruhr Univ Bochum Fak Math D-44780 Bochum Germany Univ Bayreuth Fak Math Phys & Informat D-95440 Bayreuth Germany Univ Hamburg Fachbereich Math D-20146 Hamburg Germany

We consider the problem of testing significance of predictors in multivariate nonparametric quantile regression. A stochastic process is proposed, which is based on a comparison of the responses with a nonparametric quantile regression estimate under the null hypothesis. It is demonstrated that under the null hypothesis this process converges weakly to a centered Gaussian process and the asymptotic properties of the test under fixed and local alternatives are also discussed. In particular we show, that - in contrast to the nonparametric approach based on estimation of L-2-distances - the new test is able to detect local alternatives which converge to the null hypothesis with any rate a(n) -> 0 such that a(n)root n -> infinity (here n denotes the sample size). We also present a small simulation study illustrating the finite sample properties of a bootstrap version of the corresponding Kolmogorov-Smirnov test.

关键词： nonparametric quantile regression significance testing empirical processes monotone rearrangement

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