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Journal articles on the topic 'Quantity quantile regression'

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Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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1

Pryce, Robert, Bruce Hollingsworth, and Ian Walker. "Alcohol quantity and quality price elasticities: quantile regression estimates." European Journal of Health Economics 20, no. 3 (October 1, 2018): 439–54. http://dx.doi.org/10.1007/s10198-018-1009-8.

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2

Forthmann, Boris, and Denis Dumas. "Quantity and Quality in Scientific Productivity: The Tilted Funnel Goes Bayesian." Journal of Intelligence 10, no. 4 (November 1, 2022): 95. http://dx.doi.org/10.3390/jintelligence10040095.

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The equal odds baseline model of creative scientific productivity proposes that the number of high-quality works depends linearly on the number of total works. In addition, the equal odds baseline implies that the percentage of high-quality works and total number of works are uncorrelated. The tilted funnel hypothesis proposes that the linear regression implied by the equal odds baseline is heteroscedastic with residual variance in the quality of work increasing as a function of quantity. The aim of the current research is to leverage Bayesian statistical modeling of the equal odds baseline. Previous work has examined the tilted funnel by means of frequentist quantile regression, but Bayesian quantile regression based on the asymmetric Laplace model allows for only one conditional quantile at a time. Hence, we propose additional Bayesian methods, including Poisson modeling to study conditional variance as a function of quantity. We use a classical small sample of eminent neurosurgeons, as well as the brms Bayesian R package, to accomplish this work. In addition, we provide open code and data to allow interested researchers to extend our work and utilize the proposed modeling alternatives.

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3

Carreño, Pia, and Andres Silva. "Fruit and vegetable expenditure disparities: evidence from Chile." British Food Journal 121, no. 6 (June 20, 2019): 1203–19. http://dx.doi.org/10.1108/bfj-06-2018-0365.

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Purpose The purpose of this paper is to explore fruit and vegetable (FV) procurement disparity across income groups. Design/methodology/approach This study uses mean comparison and quintile regression to explain FVs variations. Findings Households from the highest income quantile spend more than two times on FVs than households from the lowest quantile; however, this expenditure disparity is largely mitigated in terms of purchase quantity. This paper presents evidence that, rather than quantity discounts or income neighborhood, the type of store (traditional markets vs supermarkets) plays a relevant role in explaining the smaller gap in terms of purchase quantity. Research limitations/implications Traditional markets help low-income households access low-cost FVs. Social implications The authors generate evidence to show that traditional markets play a relevant role to supply affordable FV to low-income households. Originality/value The paper used a high-quality and uncommon data set. It is a topic of high social impact.

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4

Idris, N., Rais Rais, and I. T. Utami. "APLIKASI REGRESI KUANTIL PADA KASUS DBD DI KOTA PALU SULAWESI TENGAH." JURNAL ILMIAH MATEMATIKA DAN TERAPAN 15, no. 1 (May 14, 2018): 108–17. http://dx.doi.org/10.22487/2540766x.2018.v15.i1.10207.

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Palu city is one of the cities with unstable changes of natural conditions. The natural conditions such as the frequency of rainy day, temperature and humidity which are always changeable bring bad impacts and will cause of diseases especially dengue hemorrhagic fever (DBD). Therefore, it needs an action to recognise whether or not the natural condition factor influences the spread of DBD and determines what factors of the natural condition can influence the spread of DBD. This research applied quantile regression in the case of DBD in Palu city. Quantile regression is an analysis technique regarding to the functional relationship between one dependent variable with one or more independent variables which can provide accurate and stable results even though there will be outliers. Based on the result of the research, it is obtained that the natural condition factor affected the spread of DBD. This is because from 3 natural conditions only 11 significant or influential quantiles on the tested data, the quantiles are 0,30; 0,35; 0,40; 0,45; 0,50; 0,55; 0,60; 0,65; 0,70; 0,75 and 0,80. Meanwhile the most influential factor of natural conditions in spreading DBD is the frequency of rainy day because it has positive which means that 1 progress of percentage will increase the quantity of DBD case.

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5

Kostakis, Ioannis, Dimitrios Paparas, Anna Saiti, and Stamatina Papadaki. "Food Consumption within Greek Households: Further Evidence from a National Representative Sample." Economies 8, no. 1 (February 25, 2020): 17. http://dx.doi.org/10.3390/economies8010017.

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The aim of this study is to characterize the relationship between food consumption and socio-demographic characteristics in several groups of individuals. This is achieved by capturing the quantity of food purchased in categories on a microeconomic level. The empirical analysis is approached through the estimation of (a) expanded generalized linear models, (b) quantile regression models, (c) quadratic almost ideal demand system models and (d) Deaton’s (1988) approach. The results reveal that the composition of a household has a significant impact on the quantity of food consumed. In addition, price and income elasticities are estimated, confirming that the majority of food items are inelastic with respect to price and income except for meat. These findings can be used as a basis for considering food policy implications while evaluating the potential gains from applying specific policies.

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6

Cao, Jialei, and Chenran Ge. "Research on the Impact of Technology Innovation on Quantity and Quality of Economic Growth in the Yangtze River Delta of China: A Comparative Study." International Journal of Sustainable Development and Planning 16, no. 8 (December 30, 2021): 1455–64. http://dx.doi.org/10.18280/ijsdp.160806.

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High-quality economic development (HQED) has recently become a crucial sustainable growth mode in China, which pursues economic growth while maintaining social equity and green ecology. The HQED of the Yangtze River Delta (YRD) has played an exemplary role in achieving the leap from “China speed” to “China Quality”. In this paper, we first use the entropy-weight multidimensional comprehensive evaluation method to calculate the HQED index as a proxy for the quality of economic growth. Then, using panel data of 41 cities in the YRD, we conduct a comparative study to examine impacts of technological innovation (TI) on quantity and quality of economic growth by employing different panel estimation models over the period 2009-2019 and check the robustness in five ways. Finally, this paper investigates the TI-economic growth link based on the panel quantile regression across the conditional distributions of economic growth levels. Results show that TI has significantly positive effects in terms of both quantity and quality of economic growth, and the promoting effect on the quantity of economic growth is almost four times higher than that of quality under mean estimations by double fixed-effects. The effect on quantity of economic growth is also stronger than that of quality under the conditional distribution, and TI has a stronger impact for regions with higher levels of economic growth.

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7

Hlubinka, Daniel, and Miroslav Šiman. "On elliptical quantiles in the quantile regression setup." Journal of Multivariate Analysis 116 (April 2013): 163–71. http://dx.doi.org/10.1016/j.jmva.2012.11.016.

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8

Shaikh, Imlak. "The Relation between Implied Volatility Index and Crude Oil Prices." Engineering Economics 30, no. 5 (December 14, 2019): 556–66. http://dx.doi.org/10.5755/j01.ee.30.5.21611.

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Crude oil is a global commodity traded across the world market. The prices of the commodity over an extended period for crude oil have been analyzed using daily prices of crude oil futures and the implied volatility index (OVX). This paper aims to find the predictability of various parameters on the basis of time using neural network and quantile regression methods. Several estimates have been shown based on Barone, Adesi, and Whaley’s (BAW) model of neural network. Estimation parameters include opening, closing, highest and lowest price of the commodity and volumes traded for a given commodity on each trading day. The neural network estimates explain that future prices of the WTI/USO can be predicted with minimal error, and similar can be used to predict future volatility. The quantile regression results suggest that crude oil prices and OVX are strongly associated. The asymmetric association between the WTI/USO and OVX explains that the volatility feedback effect holds good for the OVX market. Bai and Perron least squares estimate evidence of the presence of a break in the time series. The main results uncover several interesting facts that implied volatility tends to remain calm during the global financial crises and higher throughout the post crisis period. The empirical outcome on the OVX market provides some practical implications for the trader and investor, in which oil futures can serve better to hedge the crude price volatility. The crude oil producer can short hedge enough through volatility futures and options to maintain the future quantity of crude to be produced.

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9

Lipovetsky, Stan. "Quantile Regression." Technometrics 48, no. 3 (August 2006): 445–46. http://dx.doi.org/10.1198/tech.2006.s410.

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10

Jurečková, Jana. "Quantile Regression." Journal of the American Statistical Association 101, no. 476 (December 1, 2006): 1723. http://dx.doi.org/10.1198/jasa.2006.s143.

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11

Das, Kiranmoy, Martin Krzywinski, and Naomi Altman. "Quantile regression." Nature Methods 16, no. 6 (May 30, 2019): 451–52. http://dx.doi.org/10.1038/s41592-019-0406-y.

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12

ALTIN YAVUZ, Arzu, and Ebru GÜNDOĞAN AŞIK. "Quantile Regression." Uluslararası Muhendislik Arastirma ve Gelistirme Dergisi 9, no. 2 (June 15, 2017): 137–46. http://dx.doi.org/10.29137/umagd.352530.

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13

Koenker, Roger, and Kevin F. Hallock. "Quantile Regression." Journal of Economic Perspectives 15, no. 4 (November 1, 2001): 143–56. http://dx.doi.org/10.1257/jep.15.4.143.

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Quantile regression, as introduced by Koenker and Bassett (1978), may be viewed as an extension of classical least squares estimation of conditional mean models to the estimation of an ensemble of models for several conditional quantile functions. The central special case is the median regression estimator which minimizes a sum of absolute errors. Other conditional quantile functions are estimated by minimizing an asymmetrically weighted sum of absolute errors. Quantile regression methods are illustrated with applications to models for CEO pay, food expenditure, and infant birthweight.

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14

Chernozhukov, Victor, Antonio F. Galvao, Xuming He, and Zhijie Xiao. "Quantile regression." Journal of Econometrics 213, no. 1 (November 2019): 1–3. http://dx.doi.org/10.1016/j.jeconom.2019.04.002.

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15

Park, Cheolwoo, Thomas C. M. Lee, and Jan Hannig. "Multiscale Exploratory Analysis of Regression Quantiles Using Quantile SiZer." Journal of Computational and Graphical Statistics 19, no. 3 (January 2010): 497–513. http://dx.doi.org/10.1198/jcgs.2010.09120.

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16

Paindaveine, Davy, and Miroslav Šiman. "Computing multiple-output regression quantile regions from projection quantiles." Computational Statistics 27, no. 1 (February 11, 2011): 29–49. http://dx.doi.org/10.1007/s00180-011-0231-y.

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17

Dodge, Yadolah, and Jana Jurečková. "Estimation of quantile density function based on regression quantiles." Statistics & Probability Letters 23, no. 1 (April 1995): 73–78. http://dx.doi.org/10.1016/0167-7152(94)00097-r.

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18

Aloqaili, Murtadha Jaafar, and Rahim Alhamzawi. "Bayesian Composite Quantile Regression with Composite Group Bridge Penalty." NeuroQuantology 20, no. 2 (February 28, 2022): 173–79. http://dx.doi.org/10.14704/nq.2022.20.2.nq22269.

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We study composite quantile regression (CQReg) with composite group bridge penalty for model selection and estimation. Compared to conventional mean regression, composite quantile regression (CQR) is an efficient and robust estimation approach. A simple and efficient algorithm was developed for posterior inference using a pseudo composite asymmetric Laplace distribution which can be formulated as a location-scale mixture of normals. The composite group bridge priors were formulated as a scale mixture of multivariate uniforms. We assess the performance of the proposed method using simulation studies, and demonstrate it with an air pollution data. Results indicated that our approach performs very well compared to the existing approaches.

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19

Hlubinka, Daniel, and Miroslav Šiman. "On generalized elliptical quantiles in the nonlinear quantile regression setup." TEST 24, no. 2 (October 18, 2014): 249–64. http://dx.doi.org/10.1007/s11749-014-0405-3.

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20

Sueyoshi, Toshiyuki. "EMPIRICAL REGRESSION QUANTILE." Journal of the Operations Research Society of Japan 34, no. 3 (1991): 250–62. http://dx.doi.org/10.15807/jorsj.34.250.

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21

Rodrigues, T., J. L. Dortet-Bernadet, and Y. Fan. "Pyramid Quantile Regression." Journal of Computational and Graphical Statistics 28, no. 3 (April 30, 2019): 732–46. http://dx.doi.org/10.1080/10618600.2019.1575225.

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22

Spokoiny, Vladimir, Weining Wang, and Wolfgang Karl Härdle. "Local quantile regression." Journal of Statistical Planning and Inference 143, no. 7 (July 2013): 1109–29. http://dx.doi.org/10.1016/j.jspi.2013.03.008.

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23

Tong, Hongzhi, and Qiang Wu. "Moving quantile regression." Journal of Statistical Planning and Inference 205 (March 2020): 46–63. http://dx.doi.org/10.1016/j.jspi.2019.06.003.

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24

Yu, Keming, and Rana A. Moyeed. "Bayesian quantile regression." Statistics & Probability Letters 54, no. 4 (October 2001): 437–47. http://dx.doi.org/10.1016/s0167-7152(01)00124-9.

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25

Chernozhukov, Victor. "Extremal quantile regression." Annals of Statistics 33, no. 2 (April 2005): 806–39. http://dx.doi.org/10.1214/009053604000001165.

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26

Dodge, Yadolah, and Joe Whittaker. "Partial quantile regression." Metrika 70, no. 1 (March 11, 2008): 35–57. http://dx.doi.org/10.1007/s00184-008-0177-4.

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27

Trzpiot, Grażyna. "Spatial Quantile Regression." Comparative Economic Research. Central and Eastern Europe 15, no. 4 (March 8, 2013): 265–79. http://dx.doi.org/10.2478/v10103-012-0040-8.

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In a number of applications, a crucial problem consists in describing and analyzing the influence of a vector Xi of covariates on some real-valued response variable Yi. In the present context, where the observations are made over a collection of sites, this study is more difficult, due to the complexity of the possible spatial dependence among the various sites. In this paper, instead of spatial mean regression, we thus consider the spatial quantile regression functions. Quantile regression has been considered in a spatial context. The main aim of this paper is to incorporate quantile regression and spatial econometric modeling. Substantial variation exists across quantiles, suggesting that ordinary regression is insufficient on its own. Quantile estimates of a spatial-lag model show considerable spatial dependence in the different parts of the distribution.

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28

Xiao, Zhijie. "Quantile cointegrating regression." Journal of Econometrics 150, no. 2 (June 2009): 248–60. http://dx.doi.org/10.1016/j.jeconom.2008.12.005.

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29

Radaelli, Paolo, and Michele Zenga. "Quantity quantiles linear regression." Statistical Methods and Applications 17, no. 4 (October 23, 2007): 455–69. http://dx.doi.org/10.1007/s10260-007-0071-7.

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30

So, Byung-Jin, Hyun-Han Kwon, and Jung-Hee An. "Trend Analysis of Extreme Precipitation Using Quantile Regression." Journal of Korea Water Resources Association 45, no. 8 (August 31, 2012): 815–26. http://dx.doi.org/10.3741/jkwra.2012.45.8.815.

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31

Kuan, Chung-Ming, Christos Michalopoulos, and Zhijie Xiao. "Quantile Regression on Quantile Ranges - A Threshold Approach." Journal of Time Series Analysis 38, no. 1 (August 10, 2016): 99–119. http://dx.doi.org/10.1111/jtsa.12204.

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32

Li, Ruosha, and Limin Peng. "Assessing quantile prediction with censored quantile regression models." Biometrics 73, no. 2 (December 8, 2016): 517–28. http://dx.doi.org/10.1111/biom.12627.

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33

Fernandes, Marcelo, Emmanuel Guerre, and Eduardo Horta. "Smoothing Quantile Regressions." Journal of Business & Economic Statistics 39, no. 1 (October 4, 2019): 338–57. http://dx.doi.org/10.1080/07350015.2019.1660177.

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34

Dang, Hung Ngoc, Pham Thi Hong Diep, and Dang Thai Binh. "Study Factors Affecting the Level of Information Disclosure of Vietnamese Enterprises." International Journal of Accounting and Financial Reporting 9, no. 2 (April 15, 2019): 199. http://dx.doi.org/10.5296/ijafr.v9i2.14662.

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This study explores the status of information disclosure and the factors affecting the disclosure of information in the annual report of listed companies in the stock market of Vietnam This study uses a combination of weighting methods, assessing the level of published information of each criterion to measure the level of information disclosure both in terms of quantity and quality. The authors use a combined approach to measure the level of disclosure in the annual report of 289 enterprises in Vietnam. In which, the authors use to test the parameters and non-parametric testing of the level of disclosure of information under the industry and according to Big4 auditing firms. At the same time, in this research, the authors apply the OLS regression and quantile regression model to examine the effect of each factor on the level of information disclosure. Research shows that the level of disclosure in the annual report is 58.57%. The research has identified four factors that affect the level of disclosure: independent audit, enterprise size, profitability, financial leverage. However, there are two factors that do not affect the level of disclosure: the number of members of the board of directors and the Chairman & General Director. This result will suggest some recommendations to help businesses, agencies to improve the level of information disclosure.

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35

Brenowitz, Willa D., Jennifer J. Manly, Audrey R. Murchland, Thu T. Nguyen, Sze Y. Liu, M. Maria Glymour, Deborah A. Levine, et al. "State School Policies as Predictors of Physical and Mental Health: A Natural Experiment in the REGARDS Cohort." American Journal of Epidemiology 189, no. 5 (October 9, 2019): 384–93. http://dx.doi.org/10.1093/aje/kwz221.

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Abstract We used differences in state school policies as natural experiments to evaluate the joint influence of educational quantity and quality on late-life physical and mental health. Using US Census microsample data, historical measures of state compulsory schooling and school quality (term length, student-teacher ratio, and attendance rates) were combined via regression modeling on a scale corresponding to years of education (policy-predicted years of education (PPYEd)). PPYEd values were linked to individual-level records for 8,920 black and 14,605 white participants aged ≥45 years in the Reasons for Geographic and Racial Differences in Stroke study (2003–2007). Linear and quantile regression models estimated the association between PPYEd and Physical Component Summary (PCS) and Mental Component Summary (MCS) from the Short Form Health Survey. We examined interactions by race and adjusted for sex, birth year, state of residence at age 6 years, and year of study enrollment. Higher PPYEd was associated with better median PCS (β = 1.28, 95% confidence interval (CI): 0.40, 1.49) and possibly better median MCS (β = 0.46, 95% CI: –0.01, 0.94). Effect estimates were higher among black (vs. white) persons (PCS × race interaction, β = 0.22, 95% CI: –0.62, 1.05, and MCS × race interaction, β = 0.18; 95% CI: –0.08, 0.44). When incorporating both school quality and duration, this quasiexperimental analysis found mixed evidence for a causal effect of education on health decades later.

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36

Ben Bouallègue, Zied. "Statistical postprocessing of ensemble global radiation forecasts with penalized quantile regression." Meteorologische Zeitschrift 26, no. 3 (June 14, 2017): 253–64. http://dx.doi.org/10.1127/metz/2016/0748.

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37

Ding, Xiaohao, Yifan Huang, Wenjuan Gao, and Weifang Min. "A Comparative Study of the Impacts of Human Capital and Physical Capital on Building Sustainable Economies at Different Stages of Economic Development." Energies 14, no. 19 (October 1, 2021): 6259. http://dx.doi.org/10.3390/en14196259.

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This study investigated the contributions of human capital and physical capital to economies at different stages by measuring the economic development with the traditional GDP and green GDP. The traditional GDP stood for the quantity of economic growth, and the green GDP, taking both the energy consumption and environmental pollution into account, was employed to represent the sustainability of economic development. We used a panel data of 143 countries and regions during the period from 1990 to 2014, and results showed that the elasticities of output with respect to human capital were greater compared to physical capital, while green GDP was significantly more sensitive to changes in human capital than the traditional GDP. In particular, considering the unbalanced distribution of economic growth among countries and regions, we employed the quantile regression model to explore the heterogeneous roles of physical and human capital in different stages of economic development, which evidenced not only the significance but also the stability of human capital. As national economic levels grew, countries became less dependent on physical capital, yet human capital maintained its outstanding role at different stages of economic development, particularly for the building of more sustainable economies.

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38

Zhang, Simin, and Zhikai Wang. "Effects of Vertical Fiscal Imbalance on Fiscal Health Expenditure Efficiency—Evidence from China." International Journal of Environmental Research and Public Health 20, no. 3 (January 23, 2023): 2060. http://dx.doi.org/10.3390/ijerph20032060.

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Improving fiscal health expenditure efficiency is an inherent requirement of the strategy of “healthy China” and “high-quality development”. The outbreak of COVID-19 has highlighted the importance of efficient health system. First, this paper systematically sorts out the multiple theoretical mechanisms of the positive and negative relationship between vertical fiscal imbalance and fiscal health expenditure efficiency. Secondly, a comprehensive index system, including the quantity and quality of medical services, is constructed, and the super-efficiency DEA model is used to measure fiscal health expenditure efficiency. There are obvious differences between eastern and western regions. Finally, the fixed effect model is constructed to carry out empirical research and it is found that the vertical fiscal imbalance in China has an overall positive and significant impact on the fiscal health expenditure efficiency, which is mainly achieved by optimizing the resources allocation between primary medical institutions and hospitals. Heterogeneity analysis shows that transfer payment scale has a corrective effect on the vertical fiscal imbalance’s effect. The result of quantile regression shows that the impact of vertical fiscal imbalance is not constant, and it gradually turns from positive to negative along with the improvement of fiscal health expenditure efficiency.

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39

Jurečková, Jana, Jan Picek, and Martin Schindler. "Empirical regression quantile processes." Applications of Mathematics 65, no. 3 (May 25, 2020): 257–69. http://dx.doi.org/10.21136/am.2020.0295-19.

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40

Yoon, Jong In. "Understanding the Quantile Regression." Korean Society of Human and Nature 3, no. 1 (June 30, 2022): 157–74. http://dx.doi.org/10.54913/hn.2022.3.1.157.

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In linear regression, the regression coefficient represents the change in the response variable produced by a one unit increase in the preditcor variable associated with that coefficient. The quantile regression parameter estimates the change in a specified quantile of the response variable produced by a one unit change in the predictor variable. In investigating the relationship between the employment growth and a set of predictors, the quantile regression allows comparing how some percentiles of the employment growth of firms may be more affected by certain firm’s characteristics than other percentiles. This is reflected in the change in the size of the regression coefficient. The quantile regression shows the effects of outliers are important when testing the Gibrat’s law.

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41

Galvao and Poirier. "Quantile Regression Random Effects." Annals of Economics and Statistics, no. 134 (2019): 109. http://dx.doi.org/10.15609/annaeconstat2009.134.0109.

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42

Méndez-Civieta, Álvaro, M. Carmen Aguilera-Morillo, and Rosa E. Lillo. "Fast partial quantile regression." Chemometrics and Intelligent Laboratory Systems 223 (April 2022): 104533. http://dx.doi.org/10.1016/j.chemolab.2022.104533.

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43

Seo, Kang-Min, Sung-Wan Bang, and Myoung-Shic Jhun. "Bootstrapping Composite Quantile Regression." Korean Journal of Applied Statistics 25, no. 2 (April 30, 2012): 341–50. http://dx.doi.org/10.5351/kjas.2012.25.2.341.

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44

Koo, Ja-Yong, Kwi Wook Park, Byung Won Kim, Kwang-Rae Kim, and Changyi Park. "Structured kernel quantile regression." Journal of Statistical Computation and Simulation 83, no. 1 (January 2013): 179–90. http://dx.doi.org/10.1080/00949655.2011.631923.

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45

Kang, Jongkyeong, Sungwan Bang, and Myoungshic Jhun. "Hierarchically penalized quantile regression." Journal of Statistical Computation and Simulation 86, no. 2 (February 27, 2015): 340–56. http://dx.doi.org/10.1080/00949655.2015.1014038.

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46

Huang, Hanwen, and Zhongxue Chen. "Bayesian composite quantile regression." Journal of Statistical Computation and Simulation 85, no. 18 (February 23, 2015): 3744–54. http://dx.doi.org/10.1080/00949655.2015.1014372.

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47

Peng, Limin, and Jason P. Fine. "Competing Risks Quantile Regression." Journal of the American Statistical Association 104, no. 488 (December 2009): 1440–53. http://dx.doi.org/10.1198/jasa.2009.tm08228.

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48

Reich, Brian J., Montserrat Fuentes, and David B. Dunson. "Bayesian Spatial Quantile Regression." Journal of the American Statistical Association 106, no. 493 (March 2011): 6–20. http://dx.doi.org/10.1198/jasa.2010.ap09237.

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49

Li, Youjuan, and Ji Zhu. "L1-Norm Quantile Regression." Journal of Computational and Graphical Statistics 17, no. 1 (March 2008): 163–85. http://dx.doi.org/10.1198/106186008x289155.

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50

Hahn, Jinyong. "Bootstrapping Quantile Regression Estimators." Econometric Theory 11, no. 1 (February 1995): 105–21. http://dx.doi.org/10.1017/s0266466600009051.

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The asymptotic variance matrix of the quantile regression estimator depends on the density of the error. For both deterministic and random regressors, the bootstrap distribution is shown to converge weakly to the limit distribution of the quantile regression estimator in probability. Thus, the confidence intervals constructed by the bootstrap percentile method have asymptotically correct coverage probabilities.

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