Bootstrapping the change-point of a hazard rate (Q688356)

The paper begins with the claim that bootstrap fails when the limiting distribution of a statistic of interest is not normal. Then a particular parametric model for a density \(f_ \theta\) is considered: \[ f_ \theta (t)= e^{-a t} I(0<t< \tau)+ e^{-a\tau- b(t-\tau)} I(t\geq\tau), \qquad \theta= (a,b,\tau), \] and \(n(\widehat {\tau}- \tau)\) is considered as the statistic of interest, where \(\widehat {\tau}\) is the MLE of \(\tau\). It is stated that the limit distribution of this statistic is of rather complicated nature. Then it is proved that this distribution coincides with it's bootstrapped version. May this reviewer remark that the limit distribution of MLE, in a different setting, when \(\tau\) is really the change-point of a sequence of independent r.v., is given, e.g., by \textit{Ts. G. Khakhubia} [Theory Probab. Appl. 31, 141-144 (1987); translation from Teor. Veroyatn. Primen. 31, No. 1, 152-155 (1986; Zbl 0609.62027)].