Numéro spécial : Special Issue on Change-Point Detection
Real time change-point detection in a model by adaptive LASSO and CUSUM
[Real time change-point detection in a model by adaptive LASSO and CUSUM]
Journal de la société française de statistique, Tome 156 (2015) no. 4, pp. 113-132.

Dans ce papier, la statistique de test CUSUM basée sur les résidus LASSO adaptatifs est proposée et étudiée pour détecter en temps réel si un changement a lieu dans un modèle linéaire qui a un nombre grand de variables explicatives.

Sous l’hypothèse nulle que le modèle ne subit pas de changements, la distribution asymptotique de la statistique de test est déterminée. Sous l’hypothèse alternative qu’un changement se produit dans le modèle à un instant inconnu, la statistique de test proposée converge en probabilité vers ∞ . Ces résultats permettent la construction d’une zone de rejet asymptotique. Ensuite, pour améliorer la performance de la statistique de test on propose une statistique de test modifiée.

Les résultats des simulations, par Monte Carlo, montrent la performance de la statistique de test proposée en la comparant aussi avec la statistique de test CUSUM classique.

In this paper, the CUSUM test statistic based on adaptive LASSO residuals is proposed and studied for detecting in real time a change-point in a linear model with a large number of explanatory variables.

Under null hypothesis that the model does not change, the asymptotic distribution of the test statistic is determined. Under alternative hypothesis that at some unknown observation there is a change in model, the proposed test statistic converges in probability to ∞ . These results allow to build an asymptotic critical region. Next, in order to improve the test statistic performance a modified test statistic is proposed.

Simulation results, using Monte Carlo technique, illustrate the performance of the proposed test statistic. We also compare it with the classical CUSUM test statistic.

Mots-clés : sequential test, adaptive LASSO, CUSUM, asymptotic behaviour 
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     title = {Real time change-point detection in a model by adaptive {LASSO} and {CUSUM}},
     journal = {Journal de la soci\'et\'e fran\c{c}aise de statistique},
     pages = {113--132},
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     volume = {156},
     number = {4},
     year = {2015},
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Ciuperca, Gabriela. Real time change-point detection in a model by adaptive LASSO and CUSUM. Journal de la société française de statistique, Tome 156 (2015) no. 4, pp. 113-132. http://www.numdam.org/item/JSFS_2015__156_4_113_0/

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