Estimation d'une rupture en dépendance faible

Let $\text{(X}{}_{\mathrm{n}}\text{,Y}{}_{\mathrm{n}}\text{)}{}_{\mathrm{<mtext>n\in </mtext><mtext>N</mtext>}}$ be a stationary sequence governed by the model Y_n=m(X_n)+σ(X_n)ε_n where $\text{(ε}{}_{\mathrm{n}}\text{)}{}_{\mathrm{<mtext>n\in </mtext><mtext>N</mtext>}}$ is i.i.d. and independent from $\text{(X}{}_{\mathrm{n}}\text{)}{}_{\mathrm{<mtext>n\in </mtext><mtext>N</mtext>}}\text{.}$ The latter sequence satisfy a weak dependence condition proposed by Doukhan and Louhichi in [2]. We provide a Central Limit Theorem for jumps in the regression function. Our method deals with linear local regression described in [4]. We use a variation on Lindeberg–Rio method as in [5]. To cite this article: P. Ango Nze, C. Prieur, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 267–270.