## The Annals of Statistics

### Local Asymptotics for Regression Splines and Confidence Regions

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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 21 June 2002

https://projecteuclid.org/euclid.aos/1024691356

Digital Object Identifier
doi:10.1214/aos/1024691356

Mathematical Reviews number (MathSciNet)
MR1673277

Zentralblatt MATH identifier
0929.62052

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

#### Citation

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. https://projecteuclid.org/euclid.aos/1024691356

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• COLUMBUS, OHIO 43210-1247 OHIO STATE UNIVERSITY E-MAIL: zhou@stat.ohio-state.edu COLUMBUS, OHIO 43210-1247