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Theory and Methods

Two-Way Truncated Linear Regression Models with Extremely Thresholding Penalization

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Pages 887-903 | Received 27 Aug 2020, Accepted 07 Nov 2022, Published online: 12 Dec 2022

References

  • Breheny, P., and Huang, J. (2011), “Coordinate Descent Algorithms for Nonconvex Penalized Regression, with Applications to Biological Feature Selection,” The Annals of Applied Statistics, 5, 232–253. DOI: 10.1214/10-AOAS388.
  • Candès, E., and Tao, T. (2007), “The Dantzig Selector: Statistical Estimation when p is much Larger than n,” The Annals of Statistics, 35, 2313–2351.
  • Chen, M., Lian, Y., Chen, Z., and Zhang, Z. (2017), “Sure Explained Variability and Independence Screening,” Journal of Nonparametric Statistics, 29, 849–883. DOI: 10.1080/10485252.2017.1375111.
  • Ciuperca, G. (2014), “Model Selection by Lasso Methods in a Change-Point Model,” Statistical Papers, 55, 349–374. DOI: 10.1007/s00362-012-0482-x.
  • 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. DOI: 10.1198/016214501753382273.
  • Fan, J., Li, R., Zhang, C.-H., and Zou, H. (2020), Statistical Foundations of Data Science, Boca Raton, FL: Chapman and Hall/CRC.
  • Fan, J., and Lv, J. (2008), “Sure Independence Screening for Ultra-High Dimensional Feature Space,” Journal of the Royal Statistical Society, Series B, 70, 849–911. DOI: 10.1111/j.1467-9868.2008.00674.x.
  • Feder, P. I. (1975), “On Asymptotic Distribution Theory in Segmented Regression Problems,” The Annals of Statistics, 3, 49–83. DOI: 10.1214/aos/1176342999.
  • Gao, M., Kong, W., Huang, Z., and Xie, Z. (2020), “Identification of Key Genes Related to Lung Squamous Cell Carcinoma using Bioinformatics Analysis,” International Journal of Molecular Sciences, 21. DOI: 10.3390/ijms21082994.
  • Hall, P., and Miller, H. (2009), “Using Generalized Correlation to Effect Variable Selection in Very High Dimensional Problems,” Journal of Computational and Graphical Statistics, 18, 533–550. DOI: 10.1198/jcgs.2009.08041.
  • Hansen, B. E. (2000), “Sample Splitting and Threshold Estimation,” Econometrica, 68, 575–603. DOI: 10.1111/1468-0262.00124.
  • Hansen, B. E. (2017), “Regression Kink with an Unknown Threshold,” Journal of Business and Economic Statistics, 35, 228–240.
  • Harchaoui, Z., and Lévy-Leduc, C. (2012), “Multiple Change-Point Estimation with a Total Variation Penalty,” Journal of the American Statistical Association, 106, 1480–1493.
  • Hinkley, D. V. (1969), “Inference about the Intersection in Two-Phase Regression,” Biometrika, 56, 495–504. DOI: 10.1093/biomet/56.3.495.
  • Kaul, A., Jandhyala, V. K., and Fotopoulos, S. B. (2019a), “An Efficient Two Step Algorithm for High Dimensional Change Point Regression Models without Grid Search,” Journal of Machine Learning Research, 20, 1–40.
  • Kaul, A., Jandhyala, V. K., and Fotopoulos, S. B. (2019b), “Detection and Estimation of Parameters in High Dimensional Multiple Change Point Regression Model via l1/l0 Regularization and Discrete Optimization,” arXiv:1906.04396.
  • Ke, Y., Li, J., and Zhang, W. (2016), “Structure Identification in Panel Data Analysis,” The Annals of Statistics, 44, 1193–1233. DOI: 10.1214/15-AOS1403.
  • Ke, Z. T., Fan, J., and Wu, Y. (2015), “Homogeneity Pursuit,” Journal of the American Statistical Association, 110, 175–194. DOI: 10.1080/01621459.2014.892882.
  • Knight, K., and Fu, W. (2000), “Asymptotics for Lasso-Type Estimators,” The Annals of Statistics, 28, 1356–1378.
  • Knowles, M., Siegmund, D., and Zhang, H. (1991), “Confidence Regions in Semilinear Regression,” Biometrika, 78, 13–31. DOI: 10.1093/biomet/78.1.15.
  • Lee, S., Seo, M. H., and Shin, Y. (2016), “The Lasso for High-Dimensional Regression with a Possible Change-Point,” Journal of the Royal Statistical Society, Series B, 78, 193–210. DOI: 10.1111/rssb.12108.
  • Leonardi, F., and Bühlmann, P. (2016), “Computationally Efficient Change Point Detection for High-Dimensional Regression,” arXiv preprint arXiv:1601.03704.
  • Li, R., Zhong, W., and Zhu, L. (2012), “Feature Screening via Distance Correlation Learning,” Journal of the American Statistical Association, 107, 1129–1139. DOI: 10.1080/01621459.2012.695654.
  • Lian, H., Qiao, X., and Zhang, W. (2021), “Homogeneity Pursuit in Single Index Models based Panel Data Analysis,” Journal of the Royal Statistical Society, Series B, 39, 386–401. DOI: 10.1080/07350015.2019.1665531.
  • Porter, J., and Yu, P. (2015), “Regression Discontinuity Designs with Unknown Discontinuity Points: Testing and Estimation,” Journal of Econometrics, 189, 132–147. DOI: 10.1016/j.jeconom.2015.06.002.
  • Siegmund, D. O., and Zhang, H. (1993), “The Expected Number of Local Maxima of a Random Field and the Volume of Tubes,” The Annals of Statistics, 21, 1948–1966. DOI: 10.1214/aos/1176349404.
  • Siegmund, D. O., and Zhang, H. (1994), “Confidence Regions in Broken Line Regression,” IMS Lecture Notes, Monograph Series, 23, 292–316.
  • Song, Z., Zhang, Y., Chen, Z., and Zhang, B. (2021), “Identification of Key Genes in Lung Adenocarcinoma based on a Competing Endogenous RNA Network,” Oncology Letters, 60. DOI: 10.3892/ol.2020.12322.
  • Tang, L., and Song, P. X. (2016), “Fused Lasso Approach in Regression Coefficients Clustering — Learning Parameter Heterogeneity in Data Integration,” Journal of Machine learning Research, 17, 1–23.
  • 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.
  • Wang, D., Zhao, Z., Lin, K., and Willet, R. (2021), “Statistically and Computationally Efficient Change Point Localization in Regression Settings,” Journal of Machine Learning Research, 22, 1–46.
  • Wang, T., and Samworth, R. J. (2018), “High Dimensional Change Point Estimation via Sparse Projection,” Journal of the Royal Statistical Society, Series B, 80, 57–83. DOI: 10.1111/rssb.12243.
  • Wang, W., Phillips, P. C., and Su, L. (2018), “Homogeneity Pursuit in Panel Data Models: Theory and Application,” Journal of Applied Econometrics, 33, 797–825. DOI: 10.1002/jae.2632.
  • Wang, W., and Su, L. (2021), “Identifying Latent Group Structures in Nonlinear Panels,” Journal of Econometrics, 220, 272–295. DOI: 10.1016/j.jeconom.2020.04.003.
  • Zhang, B., Geng, J., and Lai, L. (2015), “Multiple Change-Points Estimation in Linear Regression Models via Sparse Group Lasso,” IEEE Transactions on Signal Processing, 63, 2209–2224. DOI: 10.1109/TSP.2015.2411220.
  • Zhang, C.-H. (2010), “Nearly Unbiased Variable Selection under Minimax Concave Penalty,” The Annals of Statistics, 38, 894–942. DOI: 10.1214/09-AOS729.
  • Zhang, Z. (2021), “Functional Effects of Four or Fewer Critical Genes Linked to Lung Cancers and New Subtypes Detected by a New Machine Learning Classifier,” Journal of Clinical Trials, 11, 001.
  • Zhang, Z. (2022), “Lift the Veil of Breast Cancers using 4 or Fewer Critical Genes,” Cancer Informatics, 21, 1–11. DOI: 10.1177/11769351221076360.
  • Zheng, S., Shi, N.-Z., and Zhang, Z. (2012), “Generalized Measures of Correlation for Asymmetry, Nonlinearity, and Beyond,” Journal of the American Statistical Association, 107, 1239–1252. DOI: 10.1080/01621459.2012.710509.
  • Zhou, J., Mu, M., Xing, Y., Xin, Z., Danting, L., Yafeng, L., Jun, X., Wangfa, H., Lijun, Z., Jing, W., and Dong, H. (2020), “Identification of Key Genes in Lung Adenocarcinoma and Establishment of Prognostic Mode,” Frontiers in Molecular Biosciences, 7. DOI: 10.3389/fmolb.2020.561456.
  • Zou, H. (2006), “The Adaptive Lasso and its Oracle Properties,” Journal of the American Statistical Association, 101, 1418–1429. DOI: 10.1198/016214506000000735.
  • Zou, H., and Hastie, T. (2005), “Regularization and Variable Selection via the Elastic Net,” Journal of the Royal Statistical Society, Series B, 67, 301–320. DOI: 10.1111/j.1467-9868.2005.00503.x.

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