A Note on Distributed Quantile Regression by Pilot Sampling and One-Step Updating

References

• Alhamzawi, R., and Ali, H. T. M. (2018), “Bayesian Quantile Regression for Ordinal Longitudinal Data,” Journal of Applied Statistics, 45, 815–828. DOI: 10.1080/02664763.2017.1315059.
   Web of Science ®Google Scholar
• Battey, H., Fan, J., Liu, H., Lu, J., and Zhu, Z. (2018), “Distributed Testing and Estimation Under Sparse High Dimensional Models,” The Annals of Statistics, 46, 1352–1382. DOI: 10.1214/17-AOS1587.
   PubMed Web of Science ®Google Scholar
• Chang, X., Lin, S.-B., and Zhou, D.-X. (2017), “Distributed Semi-Supervised Learning With Kernel Ridge Regression,” Journal of Machine Learning Research, 18, 1493–1514.
   Web of Science ®Google Scholar
• Chen, C. W., Dunson, D. B., Reed, C., and Yu, K. (2013), “Bayesian Variable Selection in Quantile Regression,” Statistics and Its Interface, 6, 261–274. DOI: 10.4310/SII.2013.v6.n2.a9.
   Web of Science ®Google Scholar
• Chen, X., Liu, W., and Zhang, Y. (2019), “Quantile Regression Under Memory Constraint,” The Annals of Statistics, 47, 3244–3273. DOI: 10.1214/18-AOS1777.
   Web of Science ®Google Scholar
• Chen, X., and Xie, M.-g. (2014), “A Split-and-Conquer Approach for Analysis of Extraordinarily Large Data,” Statistica Sinica, 24, 1655–1684.
   Web of Science ®Google Scholar
• Dünner, C., Parnell, T., Atasu, K., Sifalakis, M., and Pozidis, H. (2017), “Understanding and Optimizing the Performance of Distributed Machine Learning Applications on Apache Spark,” in 2017 IEEE International Conference on Big Data (Big Data), Boston, MA: IEEE, pp. 331–338. DOI: 10.1109/BigData.2017.8257942.
   Google Scholar
• Fan, J. (2000), “Prospects of Nonparametric Modeling,” Journal of the American Statistical Association, 95, 1296–1300. DOI: 10.1080/01621459.2000.10474334.
   Web of Science ®Google Scholar
• Fan, J., and Marron, J. S. (1992), “Best Possible Constant for Bandwidth Selection,” The Annals of Statistics, 20, 2057–2070. DOI: 10.1214/aos/1176348902.
   Web of Science ®Google Scholar
• Fan, J., Wang, D., Wang, K., and Zhu, Z. (2019), “Distributed Estimation of Principal Eigenspaces,” The Annals of Statistics, 47, 3009–3031. DOI: 10.1214/18-AOS1713.
   PubMed Web of Science ®Google Scholar
• He, X., and Liang, H. (2000), “Quantile Regression Estimates for a Class of Linear and Partially Linear Errors-in-Variables Models,” Statistica Sinica, 10, 129–140.
   Web of Science ®Google Scholar
• Jia, D., Bhimani, J., Nguyen, S. N., Sheng, B. and Mi, N. (2019), “Atumm: Auto-Tuning Memory Manager in Apache Spark,” in 2019 IEEE 38th International Performance Computing and Communications Conference (IPCCC), London, UK: IEEE, pp. 1–8. DOI: 10.1109/IPCCC47392.2019.8958724.
   Google Scholar
• Jiang, J. (2010), Large Sample Techniques for Statistics, Springer Science & Business Media.
   Google Scholar
• Jordan, M. I., Lee, J. D., and Yang, Y. (2019), “Communication-Efficient Distributed Statistical Inference,” Journal of the American Statistical Association, 114, 668–681. DOI: 10.1080/01621459.2018.1429274.
   Web of Science ®Google Scholar
• Kitagawa, G., and Konishi, S. (2010), “Bias and Variance Reduction Techniques for Bootstrap Information Criteria,” Annals of the Institute of Statistical Mathematics, 62, 209–234. DOI: 10.1007/s10463-009-0237-1.
   Web of Science ®Google Scholar
• Kleiner, A., Talwalkar, A., Sarkar, P. and Jordan, M. I. (2014), “A Scalable Bootstrap for Massive Data,” Journal of the Royal Statistical Society, Series B, 76, 795–816. DOI: 10.1111/rssb.12050.
   Google Scholar
• Koenker, R. (2005), Quantile Regression, Cambridge, MA: Cambridge University Press.
   Google Scholar
• Koenker, R., and Bassett Jr, G. (1978), “Regression Quantiles,” Econometrica, 46, 33–50. DOI: 10.2307/1913643.
   Web of Science ®Google Scholar
• Koenker, R., and Hallock, K. F. (2001), “Quantile Regression,” Journal of Economic Perspectives, 15, 143–156. DOI: 10.1257/jep.15.4.143.
   Web of Science ®Google Scholar
• Koenker, R., and Park, B. J. (1996), “An Interior Point Algorithm for Nonlinear Quantile Regression,” Journal of Econometrics, 71, 265–283. DOI: 10.1016/0304-4076(96)84507-6.
   Web of Science ®Google Scholar
• Kostov, P., and Davidova, S. (2013), “A Quantile Regression Analysis of the Effect of Farmers’s Attitudes and Perceptions on Market Participation,” Journal of Agricultural Economics, 64, 112–132. DOI: 10.1111/j.1477-9552.2012.00366.x.
   Web of Science ®Google Scholar
• Lee, J. D., Liu, Q., Sun, Y., and Taylor, J. E. (2017), “Communication-Efficient Sparse Regression,”’ Journal of Machine Learning Research, 18, 115–144.
   Web of Science ®Google Scholar
• Li, G., Li, Y., and Tsai, C.-L. (2015), “Quantile Correlations and Quantile Autoregressive Modeling,” Journal of the American Statistical Association, 110, 246–261. DOI: 10.1080/01621459.2014.892007.
   Web of Science ®Google Scholar
• Li, Q., and Racine, J. S. (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.
   Google Scholar
• Li, X., Li, R., Xia, Z., and Xu, C. (2020), “Distributed Feature Screening Via Componentwise Debiasing,” Journal of Machine Learning Research, 21, 1–32.
   PubMed Web of Science ®Google Scholar
• Liu, Q., and Ihler, A. T. (2014), “Distributed Estimation, Information Loss and Exponential Families,” Advances in Neural Information Processing Systems, 1098–1106.
   Google Scholar
• Marcu, O.-C., Costan, A., Antoniu, G. and Pérez-Hernández, M. S. (2016), “Spark Versus Flink: Understanding Performance in Big Data Analytics Frameworks,” in 2016 IEEE International Conference on Cluster Computing (CLUSTER), Taipei, Taiwan: IEEE, pp. 433–442. DOI: 10.1109/CLUSTER.2016.22.
   Google Scholar
• Nguyen, N., Khan, M. M. H. and Wang, K. (2018), “Towards Automatic Tuning of Apache Spark Configuration,” in 2018 IEEE 11th International Conference on Cloud Computing (CLOUD), San Francisco, CA: IEEE, pp. 417–425. DOI: 10.1109/CLOUD.2018.00059.
   Google Scholar
• Portnoy, S., Koenker, R. et al. (1997), “The Gaussian Hare and the Laplacian Tortoise: Computability of Squared-Error Versus Absolute-Error Estimators,” Statistical Science, 12, 279–300. DOI: 10.1214/ss/1030037960.
   Web of Science ®Google Scholar
• Reich, B. J., Fuentes, M., and Dunson, D. B. (2011), “Bayesian Spatial Quantile Regression,” Journal of the American Statistical Association, 106, 6–20. DOI: 10.1198/jasa.2010.ap09237.
   PubMed Web of Science ®Google Scholar
• Shao, J. (2003), Mathematical Statistics, New York: Springer-Verlag.
   Google Scholar
• Silverman, B. W. (2018), Density Estimation for Statistics and Data Analysis, Routledge.
   Google Scholar
• Simpson, D. G., Ruppert, D., and Carroll, R. J. (1992), “On One-Step GM Estimates and Stability of Inferences in Linear Regression,” Journal of the American Statistical Association, 87, 439–450. DOI: 10.1080/01621459.1992.10475224.
   Web of Science ®Google Scholar
• Tibshirani, R. (1996), “Regression Shrinkage and Selection Via the Lasso,” Journal of the Royal Statistical Society, Series B, 58, 267–288. DOI: 10.1111/j.2517-6161.1996.tb02080.x.
   Google Scholar
• Vohra, D. (2016), “Apache Parquet,” in Practical Hadoop Ecosystem, Berkeley, CA: Springer, pp. 325–335.
   Google Scholar
• Wang, H., Li, G., and Jiang, G. (2007), “Robust Regression Shrinkage and Consistent Variable Selection Through the Lad-Lasso,” Journal of Business & Economic Statistics, 25, 347–355.
   Web of Science ®Google Scholar
• Wang, X., Yang, Z., Chen, X., and Liu, W. (2019), “Distributed Inference for Linear Support Vector Machine,” Journal of Machine Learning Research, 20, 1–41.
   Web of Science ®Google Scholar
• Xu, G., Sit, T., Wang, L., and Huang, C.-Y. (2017), “Estimation and Inference of Quantile Regression for Survival Data Under Biased Sampling,” Journal of the American Statistical Association, 112, 1571–1586. DOI: 10.1080/01621459.2016.1222286.
   PubMed Web of Science ®Google Scholar
• Zaharia, M., Xin, R. S., Wendell, P., Das, T., Armbrust, M., Dave, A., Meng, X., Rosen, J., Venkataraman, S., Franklin, M. J., Ghoshi, A., Gonzalez, J., Shenker, S., and Ion, S. (2016), ‘‘Apache Spark: A Unified Engine for Big Data Processing,” Communications of the ACM, 59, 56–65. DOI: 10.1145/2934664.
   Web of Science ®Google Scholar
• Zhang, Y., Duchi, J. C., and Wainwright, M. J. (2013), “Communication-Efficient Algorithms for Statistical Optimization,” Journal of Machine Learning Research, 14, 3321–3363.
   Web of Science ®Google Scholar
• Zhong, W., Wan, C., and Zhang, W. (2021), “Estimation and Inference for Multi-Kink Quantile Regression,” Journal of Business & Economic Statistics, 1–17.
   Web of Science ®Google Scholar
• Zhu, X., Li, F., and Wang, H. (2021), “Least-Square Approximation for a Distributed System,” Journal of Computational and Graphical Statistics. DOI: 10.1080/10618600.2021.1923517.
   Web of Science ®Google Scholar
• Zou, H., and Li, R. (2008), “One-Step Sparse Estimates in Nonconcave Penalized Likelihood Models,” The Annals of Statistics, 36, 1509–1533.
   PubMed Web of Science ®Google Scholar