Jump-detection and curve estimation methods for discontinuous regression functions based on the piecewise B-spline function

摘要

Jump-detection and curve estimation methods for the discontinuous regression function are proposed in this article. First, two estimators of the regression function based on B-splines are considered. The first estimator is obtained when the knot sequence is quasi-uniform; by adding a knot with multiplicity p + 1 at a fixed point x(0) on support [a, b], we can obtain the second estimator. Then, the jump locations are detected by the performance of the difference of the residual sum of squares DRSS(x(0)) (x(0) (a, b)); subsequently the regression function with jumps can be fitted based on piecewise B-spline function. Asymptotic properties are established under some mild conditions. Several numerical examples using both simulated and real data are presented to evaluate the performance of the proposed method.