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

Guo-Xiang Liu, Meng-Meng Wang, Xiu-Li Du, Jin-Guan Lin and Qi-Bing Gao

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 23, 5729-5749

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 x0 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(x0) (x0 ∈ (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.

Date: 2018
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DOI: 10.1080/03610926.2017.1400061

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