Polynomial Spline Confidence Bands for Regression Curves. http://www.msu.edu/˜ yangli/bandfull.pdf

Abstract: Asymptotically exact and conservative confidence bands are obtained for non-parametric regression function, using piecewise constant and piecewise linear spline estimation, respectively. Compared to the pointwise confidence interval of Huang (2003), the confidence bands are inflated by a factor of {log (n)}1/2, with the same width order as the Nadaraya-Watson bands of Härdle (1989), the local polynomial bands of Xia (1998) and Claeskens and Van Keilegom (2003). Simulation experiments provide strong evidence that corroborates with the asymptotic theory. The linear spline bands has been applied to identify an appropriate polynomial trend for fossil data