The M-estimation in a multi-phase random nonlinear model

Gabriela Ciuperca (1, 2)

1 ICJ - Institut Camille Jordan
2 PSPM - Probabilités, statistique, physique mathématique

This paper considers M-estimation of a nonlinear regression model with multiple change-points occuring at unknown times. The multi-phase random design regression model, discontinuous in each change-point, have an arbitrary error $\varepsilon$. In the case when the number of jumps is known, the M-estimator of locations of breaks and of regression parameters are studied. These estimators are consistent and the distribution of the regression parameter estimators is Gaussian. The estimator of each change-point converges, with the rate $n^{-1}$, to the smallest minimizer of the independent compound Poisson processes. The results are valid for a large class of error distributions.

Domaines: Mathématiques [math]; Statistiques [stat]; Théorie [stat.TH]

Gabriela Ciuperca. The M-estimation in a multi-phase random nonlinear model. Statistics and Probability Letters, 2009, 79 (5), pp.573-580. ⟨10.1016/j.spl.2008.10.003⟩. ⟨hal-00864838⟩