Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 3
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Fan, Yanqin and Liu, Ruixuan 2016. A direct approach to inference in nonparametric and semiparametric quantile models. Journal of Econometrics, Vol. 191, Issue. 1, p. 196.

    Kaplan, David M. 2015. Improved quantile inference via fixed-smoothing asymptotics and Edgeworth expansion. Journal of Econometrics, Vol. 185, Issue. 1, p. 20.

    Zhou, Zhou and Shao, Xiaofeng 2013. Inference for linear models with dependent errors. Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 75, Issue. 2, p. 323.



  • S.C. Goh (a1) and K. Knight (a1)
  • DOI:
  • Published online: 01 October 2009

It is well known that conventional Wald-type inference in the context of quantile regression is complicated by the need to construct estimates of the conditional densities of the response variables at the quantile of interest. This note explores the possibility of circumventing the need to construct conditional density estimates in this context with scale statistics that are explicitly inconsistent for the underlying conditional densities. This method of studentization leads conventional test statistics to have limiting distributions that are nonstandard but have the convenient feature of depending explicitly on the user’s choice of smoothing parameter. These limiting distributions depend on the distribution of the conditioning variables but can be straightforwardly approximated by resampling.

Corresponding author
*Address correspondence to S.C. Goh, Department of Economics, University of Toronto, Max Gluskin House, 150 St. George Street, Toronto, Ontario, Canada M5S 3G7; e-mail:
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

G. Bassett & R. Koenker (1978) Asymptotic theory of least absolute error regression. Journal of the American Statistical Association 73, 618622.

M Buchinsky . (1995) Estimating the asymptotic covariance matrix for quantile regression models: A Monte Carlo study. Journal of Econometrics 68, 303338.

D. De Angelis , P. Hall , & G.A. Young (1993) Analytical and bootstrap approximations to estimator distributions in L1 regressions. Journal of the American Statistical Association 88, 13101316.

C. Gutenbrunner & J. Jurečková (1992) Regression rank scores and regression quantiles. Annals of Statistics 20, 305330.

W. Hendricks & R. Koenker (1992) Hierarchical spline models for conditional quantiles and the demand for electricity. Journal of the American Statistical Association 87, 5868.

J.L Horowitz . (1998) Bootstrap methods for median regression models. Econometrica 66, 13271351.

R. Koenker & J.A.F. Machado (1999) Goodness of fit and related inference processes for quantile regression. Journal of the American Statistical Association 94, 12961310.

R. Koenker & Z. Xiao (2002) Inference on the quantile regression process. Econometrica 70, 15831612.

A.B Mukhin . (1985) Local limit theorems for distributions of sums of independent random vectors. Theory of Probability and Its Applications 29, 369375.

A.B Mukhin . (1991) Local limit theorems for lattice random variables. Theory of Probability and Its Applications 36, 698713.

S Portnoy . (1991) Asymptotic behavior of the number of regression quantile breakpoints. SIAM Journal on Scientific and Statistical Computing 12, 867883.

A. Sakov & P.J. Bickel (2000) An Edgeworth expansion for the m out of n bootstrapped median. Statistics and Probability Letters 49, 217223.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
Please enter your name
Please enter a valid email address
Who would you like to send this to? *