| A data set consists of independent observations taken at the nodes of a grid. An unknown boundary ;A class of nonparametric estimators is proposed. We obtain string consistency for these estimators (including rates of convergence and a bound on the error probability). The boundary estimate is selected from an appropriate collection ;In practice, one may be faced with a ;The boundary-estimation problem has applications in diverse fields, including: quality control, epidemiology, forestry, marine science, meteorology, and geology. Our method provides (as special cases) nonparametric estimators for the following situations: the change-point problem; the epidemic-change model; templates; linear bisection of the plane; Lipschitz boundaries. Each of these applications is explicitly analysed.;A simulation study provides numerical evidence that the boundary estimators work well. In these simulations, the two distributions actually share the same mean, median, variance, and skewness. As an illustration, a boundary estimate is calculated on a data-grid of U.S. cancer mortality rates. A non-standard bootstrap procedure is proposed for studying the variability of the boundary estimator. Simulations of this bootstrap procedure in the linear bisection case are used to construct "indifference zones". In our examples these zones seem to accurately reflect the true variability of the boundary estimator. |
