Estimation in a change-point non linear quantile model

Abstract

This paper considers a nonlinear quantile model with change-points. The quantile estimation method, which as a particular case includes median model, is more robust with respect to other traditional methods when model errors contain outliers. Under relatively weak assumptions, the convergence rate and asymptotic distribution of change-point and of regression parameter estimators are obtained. Numerical study by Monte Carlo simulations shows the performance of the proposed method for nonlinear model with change-points.

Real time change-point detection in a nonlinear quantile model

“…Assumption (A2) is considered by Zhou et al (2015) for real time detection of a change in a linear quantile model, when f ′ is bounded in the neighbourhood of X t i β 0 . Obviously, assumption (A5) is needed only in nonlinear models, so, it is for example in multiple structural change-point nonlinear quantile model, considered by Ciuperca (2016), but in a stronger assumption: for all β ∈ B, x ∈ Υ, it is imposed that .. g(x; β) 1 is bounded.…”

“…While most of the contributions to change-point model have been focused on the linear models, Ciuperca (2013) considers the sequential detection of a change-point in a nonlinear model based on CUSUM of the least squares residuals. For a posteriori change-point nonlinear model, Boldea and Hall (2013) consider the least square method, Ciuperca and Salloum (2015) consider the empirical likelihood test and Ciuperca (2016) the quantile method. In this paper, the sequential change-point detection in a nonlinear model is studied, when the errors don't satisfy the classical conditions.…”