Jump-detection and curve estimation methods for discontinuous regression functions based on the piecewise B-spline function. Issue 23 (2nd December 2018) - Liu, Guo-Xiang; Wang, Meng-Meng; Du, Xiu-Li; Lin, Jin-Guan; Gao, Qi-Bing
ABSTRACT: 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.