  We consider the problem of locating a jump discontinuity (change-point) in a
smooth parametric regression model with a bounded covariate. It is assumed that
one can sample the covariate at different values and measure the corresponding
responses. Budget constraints dictate that a total of $n$ such measurements can
be obtained. A multistage adaptive procedure is proposed, where at each stage
an estimate of the change point is obtained and new points are sampled from its
appropriately chosen neighborhood. It is shown that such procedures accelerate
the rate of convergence of the least squares estimate of the change-point.
Further, the asymptotic distribution of the estimate is derived using empirical
processes techniques. The latter result provides guidelines on how to choose
the tuning parameters of the multistage procedure in practice. The improved
efficiency of the procedure is demonstrated using real and synthetic data. This
problem is primarily motivated by applications in engineering systems.
