【作者】 陈青；

【导师】 杜秀丽；

【作者基本信息】 南京师范大学 ， 统计学， 2018， 硕士

【摘要】 不连续的回归函数,即回归函数带跳的情形广泛存在于经济生活的各个领域。而跳点的出现,往往伴随着一系列重大问题的发生,对人类的经济生活产生重大影响。如果能够找出其中可能的跳点,就能帮助人们更好的识别机遇、规避风险。样条方法具有计算速度快、稳定性好、光滑性好等优点。因此,针对不连续回归函数,本文提出了一种基于B样条函数的跳点检测和曲线估计方法。我们考虑基于B样条的两个估计量,首先,在节点序列满足拟均匀序列情形下得到第一个估计量。然后,我们在支撑集[a,b]上的固定点x处增加重复节点,使其具有p+1的重复度,由此得到第二个估计量。对于任意的x ∈(a,b),我们都可以通过计算得到关于两个估计量的残差平方和的差分(记为DRSS(x))。最终,基于DRSS(x)的性质,我们可以检测出跳点的位置,同时基于分段连续B样条函数拟合出带跳回归函数的曲线。更多还原

【Abstract】 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.更多还原