2008 03 No.90 89-96
分位数回归技术综述
基金项目(Foundation):
教育部人文社科重点研究基地基金项目《中国地区间收入分配差异与劳动力转移的经济增长效应分析》(07JJD790145);;
教育部人文社科研究基金项目《数据挖掘中关联规则的统计研究和应用》(2006JA910003)
邮箱(Email):
DOI:
中文作者单位:
厦门大学宏观经济研究中心,厦门大学宏观经济研究中心 福建厦门361005,福建厦门361005
摘要(Abstract):
普通最小二乘回归建立了在自变量X=x下因变量Y的条件均值与X的关系的线性模型。而分位数回归(Quantile Regression)则利用自变量X和因变量Y的条件分位数进行建模。与普通的均值回归相比,它能充分反映自变量X对于因变量Y的分布的位置、刻度和形状的影响,有着十分广泛的应用,尤其是对于一些非常关注尾部特征的情况。文章介绍了分位数回归的概念以及分位数回归的估计、检验和拟合优度,回顾了分位数回归的发展过程以及其在一些经济研究领域中的应用,最后做了总结。
关键词(KeyWords):
OLS回归;;分位数回归;;估计;;检验;;应用
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参考文献
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[43]Bassett G,Chen H.Quantile style:return-based attribution using regression quantiles[J].Empirical Economics,2001,26:7-40.
[44]Barnes M,Hughes A.A quantile regression analysis of the cross section of stock market return[R].Working paper,FederalReserve Bank of Boston,2002.
[45]Ma l,Pohlman L.Return forecasts and optimal portfolio construction:a quantile regression approach[R].SSRN Workingpaper 880478,2005.
[46]Engle R F,Manganelli S.CAViaR:conditional autoregressive value at risk by regression quantiles[J].Journal of Businessand Economic Statistics,2004,22:367-381.
[47]Taylor J.A quantile regression approach to qstimating the distribution of multi-period returns[J].Journal of Derivatives,1999(Fall):64-78.
[48]Chernozhukov V,Umantsev L.Conditional value at risk:aspects of modelling and estimation[J].Empirical Economics,2001,3:271-292.
[49]Chen M Y,Chen J E.Statistical inferences in quantile regression models:primal and dual aspects[R].Manuscript,2001.
[50]Georios K,Leonidas Z.Conditional autoregression quantiles:estimating market risk for major stock markets[C].The SecondInternational Symposium“Advances in Financial Forecasting”,2005.
[51]Koenker R,Hallock K F.Quantile regression:an introduction[J].Journal of Economic Perspectives,2001,15:143-156.
[52]Koenker R.Quantile regression[M].Cambridge:Cambridge University Press,2005,London.
[53]Chen C,Wei Y.Computation issues on quantile regression[J].Sankhya,2005,67:399-417.
[54]Yu K,Lu Z,Stander J.Quantile regression:applications and current research area[J].The Statistician,2003,52:331-350.
[2]Koenker R,Machado A F.Goodness of fit and related inference processes for quantile regression[J].JASA,1999,94:1296-1310.
[3]Chen C.Growth charts of body mass index(BMI)with quantile regression[R].MS.2004.
[4]Koenker R,Orey D.Computing regression quantiles[J].Applied Statistics,1993,43:410-414.
[5]Barrodale I,Roberts F D K.An improved algorithm for discrete l1linear approximation[J].SIAM J.Numer.Anal.,10:839-848.
[6]Karmarker N.A new polynomial time algorithm for linear programming[J].Combinatorica,1984,4:373-395.
[7]Portnoy S,Koenker R.The Gaussian hare and the Laplacian Tortoise:computability of squared-error versus absolute-errorestimators[J].Stat.Science,1997,12:279-300.
[8]Madsen K,Nielsen H B.A finite smoothing algorithm for liner L1 estimation[J].SIAM J.Optimization,1993,3:223-235.
[9]Chen C.An adaptive algorithm for quantile regression[C]//Thoery and Applications of Recent Robust Methods.Hubert M,Pison G,Struyf A,Van S Aelst,Series:Statistics for Industry and Technology,Birkhauser,Basel,2004,39-48.
[10]Yu K,Jones M C.Local linear quantile regression[J].JASA,1999,90:1257-1270.
[11]Green P J,Silverman B W.Nonparametric regression and generalized linear models:a roughness penalty approach[M].Chapman Hall,New York,1994.
[12]Koenker R,Ng P,Portnoy S.Quantile smoothing splines[J].Biometrika,1994,81:673-680.
[13]Yu K.Smoothing regression quantile by combining k-NN estimation with local kernel fitting[J].Statistica Sinica,1999,9:759-774.
[14]Bhattacharya P K,Gangopadhyay A K.Kernel and nearest neighbour quantile regression model[J].Econometrica,1990,66:627-651.
[15]Koenker R.Confidence intervals for quantile regression[M].In Asymptotic Statistics:Proceeding of the 5th Prague Sympo-sium on Asymptotic Statistics.Edited by M.Huskova,Physica-Velag,1994.
[16]Parzen M I,Wei L J,Ying Z.A resampling method based on pivotal estimating functions[J].Biometrika,1994,81:341-350.
[17]He X,Hu F.Markov chain marginal Bootstrap[J].JASA,2002,97:783-795.
[18]Koenker R,Hallock K.Quantile regression:an introduction[J].Journal of Economic Perspectives,2001,15:143-156.
[19]Chock D P,Winkler S L,Chen C.A study of the association between daily mortality and ambient air pollutant concentrationsin Pittsburgh,Pennsylvania[J].Journal of the Air and Waste Management Association,2000,50:1481-1500.
[20]Hilary M G,Andrzej S K.Modelling weather data by approximate regression quantiles[J].ANIZIAM J.,2003,44(E):229-248.
[21]Koneker R,Schorfheide F.Quantile spline models for global temperature change[J].Climate Change,1994,28:395-404.
[22]Dunham J B,Cade B S,Terrell J W.Influences of spatial and temporal variation on fish-habitat relationships defined byregression quantiles[J].Transactions of the American Fisheries Society,2002,131:86-98.
[23]Cole T J,Green P J.Smoothing reference centile curves:the LMS method and penalized likelihood[J].Statistics inMedicine,1992,11:1305-1319.
[24]Royston P,Altman D G.Regression using fractional polynomials for continuous covariates:parsimonious parametric modelling(with discussion)[J].Applied Statistics,1994,43:429-467.
[25]Buchinsky M.Changes in US wage structure 1963-1987:an application of quantile resression[J].Econometrica,1994,62:405-458.
[26]Schultz T,Mwabu G.Labour unions and the distribution of wages and employment in South Africa[J].Ind.and Labor Rela-tions Rev.,1998,51:680-703.
[27]Montenegro C.The structure of wages in Chile 1960-1996:an application of quantile regression[J].Estudios de Economia,1998,25:71-98.
[28]Fitzenberger B,Kurz C.New insights on earnings trends across skill groups and industries in West Germany[J].EmpiricalEconomics,2003,28(3):479-514.
[29]Fitzenberger B,Hujer R,MaCurdy T,Schnabel R.Testing for uniform wage trends in West-Germany:A cohort analysisusing quantile regressions for censored data[J].Empirical Economics,2001,26(1):41-86.
[30]Machado J A F,Mata J.Counterfactual decomposition of changes in wage distributions using quantile regression[J].Journalof Applied Econometrics 2005,4:445-465.
[31]Yu K,Philipe G,Zhang J.Bayesian quantile regression:an appication to the wage distribution in 1990s Britain[J].Sankhya,2005,67:359-377.
[32]Angrist J,Chernozhukov V,Fernandez-val I.Quantile regression under misspecification,with an application to the U.S.wage structure[J].Econometrica,2006,74(2):539-564.
[33]Papapetrou E.The unequal distribution of the public-private sector wage gap in Greece:evidence from quantile regression[J].Applied Economics Letters,2006,13(4):205-210.
[34]Deaton A.The analysis of household surveys:a microeconometric approach to development policy[M].Johns HopkinsUniversity Press,Baltimore,MD,1997.
[35]Hendricks W,Koenker R.Hierarchical spline models for conditional quantiles and the demand for electricity[J].JASA,1991,87:58-68.
[36]Manning W,Blumberg L,Moulton L.The demand for alcohol:the differential response to price[J].Journal of HealthEconomics,1995,14:123-148.
[37]Taylor J.Forecasting daily supermarket sales using exponentially weighted quantile regression[J].European Journal ofOperational Research,2007,178:154-167.
[38]Gosling A,Machin S,Meghir C.What has happened to the wages of men since 1966?[C]//Hills J.New Inequalities:theChanging Distribution of Income and Wealth in the United Kingdom.1996.
[39]Conley T,Galenson D.Nativity and wealth in mid-nineteenth-century cities[J].Journal of Economic History,1998,58:468-493.
[40]Trede M.Making mobility visible:a graphical device[J].Economics Letters,1998,59:77-82.
[41]Morillo D.Income mobility with nonparametric quantiles:a comparison of the U.S.and Germany[R].Working paper,2000.
[42]Bassett G,Chen H.Quantile style:quantiles to assess mutual fund investment styles[R].Presented at the InternationalConference on Economic Applications of Quantile Regression,Konstanz,2000.
[43]Bassett G,Chen H.Quantile style:return-based attribution using regression quantiles[J].Empirical Economics,2001,26:7-40.
[44]Barnes M,Hughes A.A quantile regression analysis of the cross section of stock market return[R].Working paper,FederalReserve Bank of Boston,2002.
[45]Ma l,Pohlman L.Return forecasts and optimal portfolio construction:a quantile regression approach[R].SSRN Workingpaper 880478,2005.
[46]Engle R F,Manganelli S.CAViaR:conditional autoregressive value at risk by regression quantiles[J].Journal of Businessand Economic Statistics,2004,22:367-381.
[47]Taylor J.A quantile regression approach to qstimating the distribution of multi-period returns[J].Journal of Derivatives,1999(Fall):64-78.
[48]Chernozhukov V,Umantsev L.Conditional value at risk:aspects of modelling and estimation[J].Empirical Economics,2001,3:271-292.
[49]Chen M Y,Chen J E.Statistical inferences in quantile regression models:primal and dual aspects[R].Manuscript,2001.
[50]Georios K,Leonidas Z.Conditional autoregression quantiles:estimating market risk for major stock markets[C].The SecondInternational Symposium“Advances in Financial Forecasting”,2005.
[51]Koenker R,Hallock K F.Quantile regression:an introduction[J].Journal of Economic Perspectives,2001,15:143-156.
[52]Koenker R.Quantile regression[M].Cambridge:Cambridge University Press,2005,London.
[53]Chen C,Wei Y.Computation issues on quantile regression[J].Sankhya,2005,67:399-417.
[54]Yu K,Lu Z,Stander J.Quantile regression:applications and current research area[J].The Statistician,2003,52:331-350.
基本信息:
DOI：
中图分类号:O212
引用信息:
[1]陈建宝,丁军军.分位数回归技术综述[J].统计与信息论坛,2008,No.90(03):89-96.
基金信息:
教育部人文社科重点研究基地基金项目《中国地区间收入分配差异与劳动力转移的经济增长效应分析》(07JJD790145);; 教育部人文社科研究基金项目《数据挖掘中关联规则的统计研究和应用》(2006JA910003)
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