Jump Detection And Curve Estimation Methods For Discontinuous Regression Functions Based On The Piecewise B Spline Function

The discontinuous regression functions,namely,the regression functions with jumps exist extensively in various fields of economic life.And the occurrence of jump points,often accompanied by a series of serious problems,has a significant impact on our daily life.If we could detect the jump points in advance,we can help people better identify the opportunity and avoid the risks.Spline method has the advantages of quick computing speed,small oscillation,as well as good smoothness.Therefore,in this paper,a jump detection and curve estimation method for the discontinuous regression function based on the B-spline function is proposed in this paper.We first consider two estimators based on the B-spline function,and the first estimator is obtained when the node sequence satisfies the quasi-uniform sequence.The second estimator is obtained by adding a knot with multiplicity p + 1 at a fixed point x on support[a,b].For any x ?(a,b),we can calculate the difference of the residual sum of squares(denoted as DRSS(x))for two estimators.Then,based on the properties of DRSS(x),we can detect the position of the jump points and the curve of the jump regression function based on the B-spline function.We also carry out numerical simulations and real analysis to verify the performance of our procedure.