9,956 | 409 | 55 |
下载次数 | 被引频次 | 阅读次数 |
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。
Abstract:Ordinary least square(OLS) regression models the relationship between vector of covariate and the conditional mean of a responsegiven.However,quantile regression models the relationship between covariateand the conditional quantiles of given.Taken together the ensemble of estimated conditional quantile offers a much more complete view of the effect of covariates on the location,scale and shape of the distribution of the response variable.It is especially useful in applications where people are interested in upper or lower quantiles of a response.In this paper we first introduce the concept of quantile regression,then provide some brief methods about estimation,hypothesis tests and goodness-of-fit of quantile regression,some important aspects of applications in economics are reviewed,a summary is given in the final section.
[1]Koenker R,Bassett G W.Regression quantiles[J].Econometrica,1978,46:33-50.
[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)