, Volume 81, Issue 6, pp 689–720 | Cite as

Test by adaptive LASSO quantile method for real-time detection of a change-point

  • Gabriela CiupercaEmail author


This article proposes a test statistic based on the adaptive LASSO quantile method to detect in real-time a change in a linear model. The model can have a large number of explanatory variables and the errors don’t satisfy the classical assumptions for a statistical model. For the proposed test statistic, the asymptotic distribution under \(H_0\) is obtained and the divergence under \(H_1\) is shown. It is shown via Monte Carlo simulations, in terms of empirical sizes, of empirical powers and of stopping time detection, that the useful test statistic for applications is better than other test statistics proposed in literature. Two applications on the air pollution and in the health field data are also considered.


Real-time detection Adaptive LASSO Quantile Asymptotic behavior 

Mathematics Subject Classification

62F05 62F35 



The author sincerely thanks the two anonymous referees, the Editor and the Associate Editor for their valuable comments which improved the quality of the paper.


  1. Ciuperca G (2013) Two tests for sequential detection of a change-point in a nonlinear model. J Stat Plann Inference 143(10):1621–1834MathSciNetCrossRefzbMATHGoogle Scholar
  2. Ciuperca G (2015) Real time change-point detection in a model by adaptive LASSO and CUSUM. Journal de la Société Francaise de Statistique 156(4):113–132MathSciNetzbMATHGoogle Scholar
  3. Ciuperca G (2016) Adaptive LASSO model selection in a multiphase quantile regression. Statistics 50(5):1100–1131MathSciNetCrossRefzbMATHGoogle Scholar
  4. Ciuperca G, Salloum Z (2016) Empirical likelihood test for high-dimensional two-sample model. J Stat Plann Inference 178:37–60MathSciNetCrossRefzbMATHGoogle Scholar
  5. Ciuperca G (2018) Adaptive group LASSO selection in quantile models. Statistical Papers. (in press to)
  6. Ciuperca G (2017) Real time change-point detection in a nonlinear quantile model. Sequ Anal 36(1):1–23MathSciNetCrossRefzbMATHGoogle Scholar
  7. Horváth L, Hušková M, Kokoszka P, Steinebach J (2004) Monitoring changes in linear models. J Stat Plann Inference 126(1):225–251MathSciNetCrossRefzbMATHGoogle Scholar
  8. Hušková M, Kirch C (2012) Bootstrapping sequential change-point tests for linear regression. Metrika 75(5):673–708MathSciNetCrossRefzbMATHGoogle Scholar
  9. Knight K, Fu W (2000) Asymptotics for LASSO-type estimators. Ann Stat 28(5):1356–1378MathSciNetCrossRefzbMATHGoogle Scholar
  10. Koenker R (2005) Quantile regression, econometric society monographs, 38. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  11. Komlós J, Major P, Tusnády G (1975) An approximation of partial sums of independent RV’s, and the sample DF. I. Z. Wahrsch. Verw. Gebiete 32:111–131MathSciNetCrossRefzbMATHGoogle Scholar
  12. Komlós J, Major P, Tusnády G (1976) An approximation of partial sums of independent RV’s, and the sample DF. II. Z. Wahrsch. Verw. Gebiete 34:33–58MathSciNetCrossRefzbMATHGoogle Scholar
  13. Lee S, Seo MH, Shin Y (2016) The lasso for high dimensional regression with a possible change point. J R Stat Soc B 78(1):193–210MathSciNetCrossRefGoogle Scholar
  14. Qian J, Su L (2016) Shrinkage estimation of regression models with multiple structural changes. Econom Theory 32(6):376–1433MathSciNetCrossRefzbMATHGoogle Scholar
  15. Tang Y, Song X, Zhu Z (2015) Variable selection via composite quantile regression with dependent errors. Stat Neerl 69(1):1–20MathSciNetCrossRefGoogle Scholar
  16. Wang X, Jiang Y, Huang M, Zhang H (2013) Robust variable selection with exponential squared loss. J Am Stat Assoc 108(502):632–643MathSciNetCrossRefzbMATHGoogle Scholar
  17. Wu Y, Liu Y (2009) Variable selection in quantile regression. Stat Sin 19(2):801–817MathSciNetzbMATHGoogle Scholar
  18. Zhou M, Wang HJ, Tang Y (2015) Sequential change point detection in linear quantile regression models. Stat Probab Lett 100:98–103MathSciNetCrossRefzbMATHGoogle Scholar
  19. Zhu LP, Zhu LX (2009) Nonconcave penalized inverse regression in single-index models with high dimensional predictors. J Multivar Anal 100:862–875MathSciNetCrossRefzbMATHGoogle Scholar
  20. Zhu LP, Qian LY, Lin JG (2011) Variable selection in a class of single-index models. Ann Inst Stat Math 63(6):1277–1293MathSciNetCrossRefzbMATHGoogle Scholar
  21. Zou H (2006) The adaptive Lasso and its oracle properties. J Am Stat Assoc 101(476):1418–1428MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CNRS, UMR 5208, Institut Camille JordanUniversité de Lyon, Université Lyon 1Villeurbanne CedexFrance

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