Statistical Papers

, Volume 55, Issue 2, pp 349–374 | Cite as

Model selection by LASSO methods in a change-point model

  • Gabriela Ciuperca
Regular Article


The paper considers a linear regression model with multiple change-points occurring at unknown times. The LASSO technique is very interesting since it allows simultaneously the parametric estimation, including the change-points estimation, and the automatic variable selection. The asymptotic properties of the LASSO-type (which has as particular case the LASSO estimator) and of the adaptive LASSO estimators are studied. For this last estimator the Oracle properties are proved. In both cases, a model selection criterion is proposed. Numerical examples are provided showing the performances of the adaptive LASSO estimator compared to the least squares estimator.


LASSO Change-points Selection criterion Asymptotic behavior Oracle properties 

Mathematics Subject Classification (2002)

62J07 62F12 


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  1. Babu GJ (1989) Strong representations for LAD estimators in linear models. Probab Theory Relat Fields 83: 547–558CrossRefzbMATHMathSciNetGoogle Scholar
  2. Bai J (1998) Estimation of multiple-regime regressions with least absolute deviation. J Stat Plan Inference 74: 103–134CrossRefzbMATHGoogle Scholar
  3. Bai J, Perron P (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66(1): 47–78CrossRefzbMATHMathSciNetGoogle Scholar
  4. Bickel PJ, Ritov Y, Tsybakov AB (2009) Simultaneous analysis of LASSO and Dantzig selector. Ann Stat 37(4): 1705–1732CrossRefzbMATHMathSciNetGoogle Scholar
  5. Ciuperca G (2009) The M-estimation in a multi-phase random nonlinear model. Stat Probab Lett 75(5): 573–580CrossRefMathSciNetGoogle Scholar
  6. Ciuperca G (2011a) Estimating nonlinear regression with and without change-points by the LAD-method. Ann Inst Stat Math 63(4): 717–743CrossRefzbMATHMathSciNetGoogle Scholar
  7. Ciuperca G (2011b) Penalized least absolute deviations estimation for nonlinear model with change-points. Stat Pap 52(2): 371–390CrossRefzbMATHMathSciNetGoogle Scholar
  8. Fan J, Li R (2001) Variable selection via nonconcave penalized likelihood and its Oracle properties. J Am Stat Assoc 96(456): 1348–1360CrossRefzbMATHMathSciNetGoogle Scholar
  9. Foster SD, Verbyla AP, Pitchford WS (2009) Estimation, prediction and inference for the LASSO random effects model. Aust N Z J Stat 51(1): 43–61CrossRefMathSciNetGoogle Scholar
  10. Harchaoui Z, Lévy-Leduc C (2010) Multiple change-point estimation with a total variation penalty. J Am Stat Assoc 105(492): 1480–1493CrossRefGoogle Scholar
  11. Kim J, Kim HJ (2008) Asymptotic results in segmented multiple regression. J Multivar Anal 99(9): 2016–2038CrossRefzbMATHGoogle Scholar
  12. Knight K, Fu W (2000) Asymptotics for LASSO-type estimators. Ann Stat 28(5): 1356–1378CrossRefzbMATHMathSciNetGoogle Scholar
  13. Koul HL, Qian L (2002) Asymptotics of maximum likelihood estimator in a two-phase linear regression model. J Stat Plan Inference 108: 99–119CrossRefzbMATHMathSciNetGoogle Scholar
  14. Pötscher BM, Schneider U (2009) On the distribution of the adaptive LASSO estimator. J Stat Plan Inference 139: 2775–2790CrossRefzbMATHGoogle Scholar
  15. Tibshirani R (1996) Regression shrinkage and selection via the LASSO. J R Stat Soc B 58: 267–288zbMATHMathSciNetGoogle Scholar
  16. Wei F, Huang J, Li H (2011) Variable selection and estimation in high-dimensional varying-coefficient models. Stat Sin 21(4). doi: 10.5705/ss.2009.316
  17. Wu Y (2008) Simultaneous change point analysis and variable selection in a regression problem. J Multivar Anal 99(9): 2154–2171CrossRefzbMATHGoogle Scholar
  18. Xu J, Ying Z (2010) Simultaneous estimation and variable selection in median regression using LASSO-type penalty. Ann Inst Stat Math 62: 487–514CrossRefMathSciNetGoogle Scholar
  19. Yao YC (1988) Estimating the number of change-points via Schwarz’s criterion. Stat Probab Lett 6: 181–189CrossRefzbMATHGoogle Scholar
  20. Zou H (2006) The adaptive LASSO and its Oracle properties. J Am Stat Assoc 101(476): 1418–1428CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

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

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