Quantile regressionestimation and lack-of-fit tests

  1. Mercedes Conde-Amboage
  2. Wenceslao González-Manteiga
  3. César Sánchez Sellero
Revista:
BEIO, Boletín de Estadística e Investigación Operativa

ISSN: 1889-3805

Ano de publicación: 2018

Volume: 34

Número: 2

Páxinas: 97-116

Tipo: Artigo

Outras publicacións en: BEIO, Boletín de Estadística e Investigación Operativa

Información de financiamento

Acknowledgements. The authors gratefully acknowledge the support of Projects MTM2013–41383–P (Spanish Ministry of Economy, Industry and Competitiveness) and MTM2016–76969–P (Spanish State Research Agency, AEI), both co–funded by the European Regional Development Fund (ERDF). Support from the IAP network StUDyS, from Belgian Science Policy, is also acknowledged.

Referencias bibliográficas

  • [1] Abberger K. 1998. Cross-validation in nonparametric quantile regression.Allgemeines Statistisches Archiv, 82: 149-161.
  • [2] Bahadur, R. R. (1966). A note on quantiles in large samples.The Annalsof Mathematical Statistics,37, 577-580.
  • [3] Barrodale, I. and Roberts, F. D. K. (1973). An improved algorithm fordiscreteL1linear approximation.SIAM Journal on Numerical Analysis,10, 839-848.
  • [4] Bloch, D. A. and Gastwirth, J. L. (1968). On a simple estimate of thereciprocal of the density function.The Annals of the Mathematical Statis-tics,39, 1083-1085.
  • [5] Bofinger, E. (1975). Estimation of a density function using order statis-tics.Australian Journal of Statistics,17, 1-7.
  • [6] Chatterjee, A. (2011). Asymptotic properties of sample quantiles from afinite population.Annals of the Institute of Statistical Mathematics,63,157 - 179.
  • [7] Chaudhuri, P. (1991a). Nonparametric estimates of regression quantilesand their local Bahadur representation.The Annals of Statistics,19,760-777.
  • [8] Chaudhuri, P. (1991b). Global nonparametric estimation of conditionalquantile functions and their derivatives.Journal of Multivariate Analysis,39, 246-269.
  • [9] Conde-Amboage, M. and S ́anchez-Sellero, C. (2018). A plug-in band-width selector for nonparametric quantile regression.TEST.https://doi.org/10.1007/s11749-018-0582-6.
  • [10] Conde-Amboage, M., S ́anchez-Sellero, C. and Gonz ́alez-Manteiga, W.(2015). A lack-of-fit test for quantile regression models with high-dimensional covariates.Computational Statistics & Data Analysis,88,128 - 138.
  • [11] Cook, R. D. and Weisberg, S. (1982). Residuals and Influence in Regres-sion.Chapman and Hall.
  • [12] Davino, C., Furno, M. and Vistocco, D. (2014).Quantile regression: the-ory and applications. John Wiley & Sons.
  • [13] Dette, H., Guhlich, M., and Neumeyer, N. (2015). Testing for additivityin nonparametric quantile regression.Annals of the Institute of StatisticalMathematics,67, 437-477.
  • [14] El Bantli, F. and Hallin, M. (1999). L1-estimation in linear models withheterogeneous white noise.Statistics & Probability Letters,45, 305-315.
  • [15] Escanciano, J.C. (2006). A consistent diagnostic test for regression mod-els using projections. Econometric Theory, 22, 1030-1051.
  • [16] Escanciano, J.C. and Goh, S.C. (2014). Specification analysis of linearquantile models. Journal of Econometrics, 178, 495-507.
  • [17] Fan, J., Hu, T. C. and Truong, Y. K. (1994). Robust nonparametricfunction estimation.Scandinavian Journal of Statistics,21, 433-446.
  • [18] El Ghouch A and Genton MG. 2012. Local polynomial quantile regres-sion with parametric features. Journal of the American Statistical Asso-ciation, 104: 1416-1429.
  • [19] Hall, P. and Sheather, S. J. (1988). On the distribution of a studentizedquantile.Journal of the Royal Statistical Society. Series B (Methodolog-ical),50, 381-391
  • [20] Hampel, F. R. (1974). The influence curve and its role in robust estima-tion.Journal of the American Statistical Association,69, 383-393.
  • [21] He, X. and Zhu, L.-X. (2003). A lack-of-fit test for quantile regression.Journal of the American Statistical Association,98, 1013-1022.
  • [22] Hendricks, W. and Koenker, R. (1992). Hierarchical spline models forconditional quantiles and the demand for electricity.Journal of the Amer-ican Statistical Association,87, 58-68.
  • [23] Horowitz, J.L. and Spokoiny, V.G. (2002). An adaptive, rate-optimaltest of linearity for median regression models.Journal of the AmericanStatistical Association,97, 822-835.
  • [24] Hyndman, R. J. and Fan, Y. (1996). Sample quantiles in statistical pack-ages.The American Statistician,50, 361 - 365.
  • [25] Koenker, R. (2005). Quantile Regression.Cambridge: Cambridge Uni-versity Press.
  • [26] Koenker, R. and Bassett, G. (1978). Regression quantiles.Econometrica,46, 33-50.
  • [27] Koenker, R. and D’Orey, V. (1987). Computing regression quantiles.Journal of the Royal Statistical Society. Series C (AppliedStatistics),36, 383-393.
  • [28] Koenker, R. and Mizera, I. (2004). Penalized triograms: total variationregularization for bivariate smoothing.Journal of the Royal StatisticalSociety. Series B (Statistical Methodology),66, 145-163.
  • [29] Koenker, R., Ng, P. and Portnoy, S. (1994). Quantile smoothing splines.Biometrika,81, 673-680.
  • [30] Maistre, S., Lavergne, P. and Patilea, V. (2017). Powerful nonparametricchecks for quantile regression.Journal of Statistical Planning and Infer-ence,180, 13 - 29.
  • [31] Maronna, R.A. and Yohai, V.J. (1981). Asymptotic behavior of generalM-estimates for regression and scale with random carriers.ProbabilityTheory and Related Fields,58, 7-20.
  • [32] Opsomer, J. D. and Ruppert, D. (1998). A fully automated bandwidthselection method for fitting additive models.Journal of the AmericanStatistical Association,93, 605-618.
  • [33] Otsu, T. (2008). Conditional empirical likelihood estimation and infer-ence for quantile regression models. Journal of Econometrics, 142, 508-538.
  • [34] Rousseeuw, P. J. (1984). Least median of squares regression.Journal ofthe American Statistical Association,79, 871-880.
  • [35] Rousseeuw, P. J. and Hubert, M. (1999). Regression depth.Journal ofthe American Statistical Association,94, 388-402.
  • [36] Ruppert D, Sheather SJ and Wand MP. 1995. An efective bandwidthselector for local least squares regression. Journal of the American Sta-tistical Association. 90: 1257-1270.
  • [37] Schwarz, G. (1978). Estimating the dimension of a model.The Annals ofStatistics,6, 461-464.
  • [38] Siddiqui, M. M. (1960). Distribution of quantiles in samples from a bivari-ate population.Journal of Research of the National Bureau of Standards,64B, 145-150.
  • [39] Stute, W. (1997). Nonparametric model checks for regression. The Annalsof Statistics, 25, 613-641.
  • [40] Tukey, J. W. (1965). Which part of the sample contains the information,Proceedings of the National Academy of Sciences,53, 127-134.
  • [41] Whang, Y.-J. (2006). Smoothed empirical likelihood methods for quantileregression models. Econometric Theory, 22, 173-205.
  • [42] Wilcox, R. R. (2008). Quantile regression: A simplified approach to agoodness-of-fit test. Journal of Data Science, 6, 547-556.
  • [43] Yu, K., and Jones, M. C. (1998). Local linear quantile regression.Journalof the American statistical Association,93, 228-237.
  • [44] Yu K and Lu Z. 2004. Local linear additive quantile regression. Scandi-navian Journal of Statistics, 31, 333-346.
  • [45] Zheng, J. X. (1996). A consistent test of functional form via nonpara-metric estimation techniques. Journal of Econometrics, 75, 263-289.
  • [46] Zheng, J. X. (1998). A consistent nonparametric test of parametricregression models under conditional quantile restrictions. EconometricTheory, 14, 123-138