Nonparametric detection of change points form observations with errors (Q1177777)

Let \(\xi_ j\), \(\eta_ j\), \(\varepsilon_ j\), \(j\in N\) be i.i.d. rv's, and let \(\kappa_ j=\xi_ j+\varepsilon_ j\), \(1\leq j\leq \vartheta N\), while \(\kappa_ j=\eta_ j+\varepsilon_ j\), \(\vartheta N\leq j\leq N\), \(\vartheta\in(0,1)\). Let \(P(\xi_ j < x)=F(x)\) and \(P(\eta_ j < x)=H(x)\), \(H\neq F\). The problem is that of estimation of \(\vartheta\). A point estimator of \(\vartheta\) is proposed and shown to be strongly consistent. Moreover, an interval estimator of \(\vartheta\) is derived, too.