Consider a parametrically specified regression model for a bounded covariate that has a single discontinuity (change point). 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. The goal is to estimate accurately the location of the change-point. A multistage procedure is proposed and its properties examined, where at each stage an estimate of the change point is obtained and new points are sampled from its neighborhood. The asymptotic distribution of the least squares estimate is derived using ideas from empirical processes. The improved efficiency of the procedure is demonstrated using real and synthetic data. Issues involved with estimation of the entire regression function are also investigated. The problem is primarily motivated by problems in engineering systems. This is joint work with George Michailidis and Yan Lan.
Group for Research in Decision Analysis