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Theory and Methods

Oracle Estimation of a Change Point in High-Dimensional Quantile Regression

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Pages 1184-1194 | Received 27 Feb 2016, Published online: 08 Jun 2018

References

  • Belloni, A., and Chernozhukov, V. (2011), “ℓ1-Penalized Quantile Regression in High Dimensional Sparse Models,” Annals of Statistics, 39, 82–130.
  • Bickel, P., Ritov, Y., and Tsybakov, A. (2009), “Simultaneous Analysis of Lasso and Dantzig Selector,” Annals of Statistics, 37, 1705–1732.
  • Bradic, J., Fan, J., and Wang, W. (2011), “Penalized Composite Quasi-Likelihood for Ultrahigh Dimensional Variable Selection,” Journal of the Royal Statistical Society, Series B, 73, 325–349.
  • Bühlmann, P., and van de Geer, S. (2011), Statistics for High-Dimensional Data, Methods, Theory and Applications, New York: Springer.
  • Callot, L., Caner, M., Kock, A. B., and Riquelme, J. A. (2017), “Sharp Threshold Detection Based on Sup-norm Error Rates in High-dimensional Models,” Journal of Business & Economic Statistics, 35, 250–264.
  • Card, D., Mas, A., and Rothstein, J. (2008), “Tipping and the Dynamics of Segregation,” Quarterly Journal of Economics, 123, 177–218.
  • Chan, K.-S. (1993), “Consistency and Limiting Distribution of the Least Squares Estimator of a Threshold Autoregressive Model,” Annals of Statistics, 21, 520–533.
  • Chan, N. H., Ing, C.-K., Li, Y., and Yau, C. Y. (2017), “Threshold Estimation via Group Orthogonal Greedy Algorithm,” Journal of Business & Economic Statistics, 35, 334–345.
  • Chan, N. H., Yau, C. Y., and Zhang, R.-M. (2014), “Group LASSO for Structural Break Time Series,” Journal of the American Statistical Association, 109, 590–599.
  • Cho, H., and Fryzlewicz, P. (2015), “Multiple-Change-Point Detection for High Dimensional Time Series via Sparsified Binary Segmentation,” Journal of the Royal Statistical Society, Series B, 77, 475–507.
  • Ciuperca, G. (2013), “Quantile Regression in High-Dimension with Breaking,” Journal of Statistical Theory and Applications, 12, 288–305.
  • Enikeeva, F., and Harchaoui, Z. (2013), “High-Dimensional Change-Point Detection with Sparse Alternatives,” arXiv preprint, http://arxiv.org/abs/1312.1900.
  • Fan, J., Fan, Y., and Barut, E. (2014), “Adaptive Robust Variable Selection,” Annals of Statistics, 42, 324–351.
  • Fan, J., and Li, R. (2001), “Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties,” Journal of the American Statistical Association, 96, 1348–1360.
  • Frick, K., Munk, A., and Sieling, H. (2014), “Multiscale Change Point Inference,” Journal of the Royal Statistical Society, Series B, 76, 495–580.
  • Fryzlewicz, P. (2014), “Wild Binary Segmentation for Multiple Change-Point Detection,” Annals of Statistics, 42, 2243–2281.
  • Hansen, B. E. (1996), “Inference When a Nuisance Parameter Is Not Identified Under the Null Hypothesis,” Econometrica, 64, 413–430.
  • ——— (2000), “Sample Splitting and Threshold Estimation,” Econometrica, 68, 575–603.
  • He, X., and Shao, Q.-M. (2000), “On Parameters of Increasing Dimensions,” Journal of Multivariate Analysis, 73, 120–135.
  • Koenker, R. (2016), quantreg: Quantile Regression, R Package Version 5.29, CRAN, available at https://cran.r-project.org/web/packages/quantreg/index.html.
  • Koenker, R., and Bassett, G. (1978), “Regression Quantiles,” Econometrica, 46, 33–50.
  • Koenker, R., and Mizera, I. (2014), “Convex Optimization in R,” Journal of Statistical Software, 60, 1–23.
  • Kosorok, M. R., and Song, R. (2007), “Inference under Right Censoring for Transformation Models with a Change-Point based on a Covariate Threshold,” Annals of Statistics, 35, 957–989.
  • Lee, S., and Seo, M. H. (2008), “Semiparametric Estimation of a Binary Response Model with a Change-Point due to a Covariate Threshold,” Journal of Econometrics, 144, 492–499.
  • Lee, S., Seo, M. H., and Shin, Y. (2011), “Testing for Threshold Effects in Regression Models,” Journal of the American Statistical Association, 106, 220–231.
  • ——— (2016), “The Lasso for High Dimensional Regression with a Possible Change Point,” Journal of the Royal Statistical Society, Series B, 78, 193–210.
  • Leonardi, F., and Bühlmann, P. (2016), “Computationally Efficient Change Point Detection for High-Dimensional Regression,” arXiv preprint arXiv:1601.03704, http://arxiv.org/abs/1601.03704.
  • Li, D., and Ling, S. (2012), “On the Least Squares Estimation of Multiple-Regime Threshold Autoregressive Models,” Journal of Econometrics, 167, 240–253.
  • Loh, P.-L., and Wainwright, M. J. (2013), “Regularized M-Estimators with Nonconvexity: Statistical and Algorithmic Theory for Local Optima,” in Advances in Neural Information Processing Systems 26, eds. C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K. Weinberger, Curran Associates, Inc., pp. 476–484.
  • Lovász, L., and Vempala, S. (2007), “The Geometry of Logconcave Functions and Sampling Algorithms,” Random Structures & Algorithms, 30, 307–358.
  • Pons, O. (2003), “Estimation in a Cox Regression Model with a Change-Point According to a Threshold in a Covariate,” Annals of Statistics, 31, 442–463.
  • Raskutti, G., Wainwright, M., and Yu, B. (2011), “Minimax Rates of Estimation for High-Dimensional Linear Regression Over ℓq-Balls,” IEEE Transactions on Information Theory, 57, 6976–6994.
  • Seijo, E., and Sen, B. (2011a), “Change-Point in Stochastic Design Regression and the Bootstrap,” Annals of Statistics, 39, 1580–1607.
  • ——— (2011b), “A Continuous Mapping Theorem for the Smallest Argmax Functional,” Electronic Journal of Statistics, 5, 421–439.
  • Tong, H. (1990), Non-Linear Time Series: A Dynamical System Approach, Oxford: Oxford University Press.
  • van de Geer, S. A. (2008), “High-Dimensional Generalized Linear Models and the Lasso,” Annals of Statistics, 36, 614–645.
  • Wang, L. (2013), “The L1 Penalized LAD Estimator for High Dimensional Linear Regression,” Journal of Multivariate Analysis, 120, 135–151.
  • Wang, L., Wu, Y., and Li, R. (2012), “Quantile Regression for Analyzing Heterogeneity in Ultra-High Dimension,” Journal of the American Statistical Association, 107, 214–222.
  • Zhao, P., and Yu, B. (2006), “On Model Selection Consistency of Lasso,” Journal of Machine Learning Research, 7, 2541–2563.
  • Zou, H., and Li, R. (2008), “One-Step Sparse Estimations in Non Concave Penalized Likelihood Models,” Annals of Statistics, 36, 1509–1533.