Computational Statistics

, Volume 29, Issue 5, pp 1129–1152 | Cite as

A sliced inverse regression approach for data stream

  • Marie Chavent
  • Stéphane Girard
  • Vanessa Kuentz-Simonet
  • Benoit Liquet
  • Thi Mong Ngoc Nguyen
  • Jérôme SaraccoEmail author
Original Paper


In this article, we focus on data arriving sequentially by blocks in a stream. A semiparametric regression model involving a common effective dimension reduction (EDR) direction \(\beta \) is assumed in each block. Our goal is to estimate this direction at each arrival of a new block. A simple direct approach consists of pooling all the observed blocks and estimating the EDR direction by the sliced inverse regression (SIR) method. But in practice, some disadvantages appear such as the storage of the blocks and the running time for large sample sizes. To overcome these drawbacks, we propose an adaptive SIR estimator of \(\beta \) based on the optimization of a quality measure. The corresponding approach is faster both in terms of computational complexity and running time, and provides data storage benefits. The consistency of our estimator is established and its asymptotic distribution is given. An extension to multiple indices model is proposed. A graphical tool is also provided in order to detect changes in the underlying model, i.e., drift in the EDR direction or aberrant blocks in the data stream. A simulation study illustrates the numerical behavior of our estimator. Finally, an application to real data concerning the estimation of physical properties of the Mars surface is presented.


Effective dimension reduction (EDR) Sliced inverse regression (SIR) Data stream 



The authors thank Sylvain Douté for his contribution to the data. They are grateful to the anonymous referees for contributing to the improvement of this paper through their useful remarks and detailed comments.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Marie Chavent
    • 1
    • 2
  • Stéphane Girard
    • 3
  • Vanessa Kuentz-Simonet
    • 4
  • Benoit Liquet
    • 5
    • 6
  • Thi Mong Ngoc Nguyen
    • 7
  • Jérôme Saracco
    • 1
    • 2
    Email author
  1. 1.Institut de Mathématiques de Bordeaux, UMR CNRS 5251Université de BordeauxTalence CedexFrance
  2. 2.CQFD TeamInria Bordeaux Sud-OuestTalence CedexFrance
  3. 3.LJK, MISTIS TeamInria Grenoble Rhône-AlpesSaint-Ismier CedexFrance
  4. 4.Unité ADBX “Aménités et Dynamiques des Espaces Ruraux”IRSTEACestas CedexFrance
  5. 5.ISPED, Centre INSERM U-897-Epidémiologie-BiostatistiqueUniversité de BordeauxBordeaux France
  6. 6.ISPED, Centre INSERM U-897-Epidémiologie-BiostatistiqueINSERMBordeaux France
  7. 7.IRMA, UMR 7501Université de Strasbourg67084 France

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