Sokbae Lee, Yuan Liao, Myung Hwan Seo, Youngki Shin
arXiv 1 Mar 2016 · Statistics — Methodology · publishedJournal of the American Statistical Association (2017) · 38 citations (OpenAlex)
arXiv:1603.00235 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop $\ell_1$-penalized estimators of both regression coefficients and the threshold parameter. Our penalized estimators not only select covariates but also discriminate between a model with homogeneous sparsity and a model with a change point. As a result, it is not necessary to know or pretest whether the change point is present, or where it occurs. Our estimator of the change point achieves an oracle property in the sense that its asymptotic distribution is the same as if the unknown active sets of regression coefficients were known. Importantly, we establish this oracle property without a perfect covariate selection, thereby avoiding the need for the minimum level condition on the signals of active covariates. Dealing with high-dimensional quantile regression with an unknown change point calls for a new proof technique since the quantile loss function is non-smooth and furthermore the corresponding objective function is non-convex with respect to the change point. The technique developed in this paper is applicable to a general M-estimation framework with a change point, which may be of independent interest. The proposed methods are then illustrated via Monte Carlo experiments and an application to tipping in the dynamics of racial segregation.
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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 | Li, D. and Ling, S (2012) On the least squares estimation of multiple-regime threshold autoregressive models | 0.928 | 4 | 3 | 100% |
| 2 | Lee, S., Seo, M. H. and Shin, Y (2016) The lasso for high dimensional regression with a possible change point self | 0.874 | 9 | 2 | 100% |
| 3 | Card, D., Mas, A. and Rothstein, J (2008) Tipping and the dynamics of segregation | 0.874 | 6 | 2 | 100% |
| 4 | Seijo, E. and Sen, B (2011) A continuous mapping theorem for the smallest argmax functional | 0.843 | 4 | 4 | 75% |
| 5 | Belloni, A. and Chernozhukov, V (2011) $_1$-penalized quantile regression in high dimensional sparse models | 0.763 | 9 | 4 | 44% |
| 6 | Pons, O (2003) Estimation in a Cox regression model with a change-point according to a threshold in a covariate | 0.737 | 3 | 3 | 67% |
| 7 | Kosorok, M. R. and Song, R (2007) Inference under right censoring for transformation models with a change-point based on a covariate threshold | 0.737 | 3 | 3 | 67% |
| 8 | Bickel, P., Ritov, Y. and Tsybakov, A (2009) Simultaneous analysis of Lasso and Dantzig selector | 0.644 | 2 | 2 | 100% |
| 9 | Hansen, B. E (1996) Inference when a nuisance parameter is not identified under the null hypothesis | 0.644 | 2 | 2 | 100% |
| 10 | Seijo, E. and Sen, B (2011) Change-point in stochastic design regression and the bootstrap | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 44 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Recovering latent linkage structures and spillover effects with structural breaks in panel data models | 0.874 | 5 | 2 |
| 2 | 2004.05127 | 0.644 | 2 | 2 |
| 3 | Sparse Quantile Regression | 0.405 | 1 | 1 |
| 4 | Two-Stage Maximum Score Estimator | 0.405 | 1 | 1 |
| 5 | Predictive Quantile Regression with Mixed Roots and Increasing Dimensions: The ALQR Approach | 0.405 | 1 | 1 |
| 6 | Uniform Inference in High-Dimensional Threshold Regression Models | 0.405 | 1 | 1 |