The Annals of Statistics

Spline Smoothing in Regression Models and Asymptotic Efficiency in $L_2$

Michael Nussbaum

Full-text: Open access

Abstract

For nonparametric regression estimation on a bounded interval, optimal rates of decrease for integrated mean square error are known but not the best possible constants. A sharp result on such a constant, i.e., an analog of Fisher's bound for asymptotic variances is obtained for minimax risk over a Sobolev smoothness class. Normality of errors is assumed. The method is based on applying a recent result on minimax filtering in Hilbert space. A variant of spline smoothing is developed to deal with noncircular models.

Article information

Source
Ann. Statist., Volume 13, Number 3 (1985), 984-997.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349651

Digital Object Identifier
doi:10.1214/aos/1176349651

Mathematical Reviews number (MathSciNet)
MR803753

Zentralblatt MATH identifier
0596.62052

JSTOR
links.jstor.org

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62G05: Estimation 41A15: Spline approximation 65D10: Smoothing, curve fitting

Keywords
Smooth nonparametric regression asymptotic minimax risk linear spline estimation boundary effects

Citation

Nussbaum, Michael. Spline Smoothing in Regression Models and Asymptotic Efficiency in $L_2$. Ann. Statist. 13 (1985), no. 3, 984--997. doi:10.1214/aos/1176349651. https://projecteuclid.org/euclid.aos/1176349651


Export citation