A jump-detecting procedure based on spline estimation

作者：Ma Shujie; Yang Lijian^*

来源：Journal of Nonparametric Statistics, 2011, 23(1): 67-81.

DOI：10.1080/10485250903571978

• B spline
• knots
• jump points
• nonparametric regression
• asymptotic Gaussian process
• asymptotic p-value
• BIC
• upcrossing probability

In a random-design nonparametric regression model, procedures for detecting jumps in the regression function via constant and linear spline estimation method are proposed based on the maximal differences of the spline estimators among neighbouring knots, the limiting distributions of which are obtained when the regression function is smooth. Simulation experiments provide strong evidence that corroborates with the asymptotic theory, while the computing is extremely fast. The detecting procedure is illustrated by analysing the thickness of pennies data set.

• 出版日期2011