The Annals of Statistics

Local Asymptotics for Regression Splines and Confidence Regions

X. Shen, D.A. Wolfe, and S. Zhou

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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.

Article information

Ann. Statist., Volume 26, Number 5 (1998), 1760-1782.

First available in Project Euclid: 21 June 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation
Secondary: 62G15: Tolerance and confidence regions 62G20: Asymptotic properties

Regression splines least squares Bernoulli polynomial asymptotic bias asymptotic variance asymptotic normality confidence interval and confidence band


Zhou, S.; Shen, X.; Wolfe, D.A. Local Asymptotics for Regression Splines and Confidence Regions. Ann. Statist. 26 (1998), no. 5, 1760--1782. doi:10.1214/aos/1024691356.

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