Fast Algorithms for the Quantile Regression Process

Chernozhukov, Victor; Fernández-Val, Iván; Melly, Blaise (2019). Fast Algorithms for the Quantile Regression Process (arXiv). Cornell University

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The widespread use of quantile regression methods depends crucially on the existence of fast algorithms. Despite numerous algorithmic improvements, the computation time is still non-negligible because researchers often estimate many quantile regressions and use the bootstrap for inference. We suggest two new fast algorithms for the estimation of a sequence of quantile regressions at many quantile indexes. The first algorithm applies the preprocessing idea of Portnoy and Koenker (1997) but exploits a previously estimated quantile regression to guess the sign of the residuals. This step allows for a reduction of the effective sample size. The second algorithm starts from a previously estimated quantile regression at a similar quantile index and updates it using a single Newton-Raphson iteration. The first algorithm is exact, while the second is only asymptotically equivalent to the traditional quantile regression estimator. We also apply the preprocessing idea to the bootstrap by using the sample estimates to guess the sign of the residuals in the bootstrap sample. Simulations show that our new algorithms provide very large improvements in computation time without significant (if any) cost in the quality of the estimates. For instance, we divide by 100 the time required to estimate 99 quantile regressions with 20 regressors and 50,000 observations.

Item Type:

Working Paper

Division/Institute:

03 Faculty of Business, Economics and Social Sciences > Department of Economics
03 Faculty of Business, Economics and Social Sciences > Department of Economics > Institute of Economics > Econometrics

UniBE Contributor:

Melly, Blaise Stéphane

Subjects:

300 Social sciences, sociology & anthropology > 330 Economics

Series:

arXiv

Publisher:

Cornell University

Language:

English

Submitter:

Dino Collalti

Date Deposited:

02 Jun 2020 14:00

Last Modified:

02 Jun 2020 14:09

ArXiv ID:

1909.05782

BORIS DOI:

10.7892/boris.138746

URI:

https://boris.unibe.ch/id/eprint/138746

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