Local Asymptotics for Regression Splines and Confidence Regions
The Annals of Statistics · 1998 · Volume 26 · Issue 5
Abstract
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.
Keywords
62G07, 62G15, 62G20, asymptotic bias, asymptotic normality, asymptotic variance, Bernoulli polynomial, confidence interval and confidence band, least squares, regression splines
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