In this paper, we study the local behavior of regression splines. In particular, explicit expressions for the asymptotic pointwise bias and variance of regression splines are obtained. In addition, asymptotic normality for regression splines is established, leading to the construction of approximate confidence intervals and confidence bands for the regression function.
"Local Asymptotics for Regression Splines and Confidence Regions." Ann. Statist. 26 (5) 1760 - 1782, October 1998. https://doi.org/10.1214/aos/1024691356