Victor Chernozhukov, Iván Fernández-Val, Blaise Melly
arXiv 12 Sep 2019 · Econometrics · publishedEmpirical Economics (2020) · 39 citations (OpenAlex)
arXiv:1909.05782 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Portnoy S, Koenker R (1997) The gaussian hare and the laplacian tortoise: computability of squared-error versus absolute-error estimators | 1.000 | 14 | 6 | 100% |
| 2 | Chernozhukov V, Hansen C (2006) Instrumental quantile regression inference for structural and treatment effect models | 1.000 | 7 | 5 | 100% |
| 3 | Chernozhukov V, Fernández-Val I, Melly B (2013) Inference on counterfactual distributions | 0.928 | 4 | 3 | 100% |
| 4 | Chernozhukov V, Fernández-Val I (2005) Subsampling inference on quantile regression processes | 0.843 | 3 | 3 | 100% |
| 5 | Belloni A, Chernozhukov V, Fernández-Val I, Hansen C (2017) Program evaluation and causal inference with high-dimensional data | 0.843 | 3 | 3 | 100% |
| 6 | Angrist J, Chernozhukov V, Fernández-Val I (2006) Quantile regression under misspecification, with an application to the us wage structure | 0.737 | 3 | 2 | 100% |
| 7 | Koenker R, Hallock KF (2001) Quantile regression | 0.644 | 4 | 1 | 100% |
| 8 | Hall P, Sheather SJ (1988) On the distribution of a studentized quantile | 0.644 | 2 | 2 | 100% |
| 9 | Koenker R, Xiao Z (2002) Inference on the quantile regression process | 0.644 | 2 | 2 | 100% |
| 10 | Machado J, Mata J (2005) Counterfactual decomposition of changes in wage distributions using quantile regression | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 43 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Fast Algorithms for Quantile Regression with Selection | 1.000 | 10 | 3 |
| 2 | Fast Inference for Quantile Regression with Tens of Millions of Observations | 0.405 | 1 | 1 |
| 3 | Conditional Rank-Rank Regression$^*$ | 0.405 | 1 | 1 |
| 4 | International vulnerability of inflation | 0.405 | 1 | 1 |
| 5 | Decomposition of Differences in Distribution under Sample Selection and the Gender Wage Gap | 0.000 | 1 | 1 |