The Annals of Statistics

The Data-Smoothing Aspect of Stein Estimates

Ker-Chau Li and Jiunn Tzon Hwang

Full-text: Open access

Abstract

The data smoothing aspect of Stein estimates is explored in the nonparametric regression settings. We show that appropriately shrinking the raw data towards any linear smoother will provide a robust "smoother" (which dominates the raw data and hence has a bounded maximum risk when the average squared error loss is concerned).

Article information

Source
Ann. Statist., Volume 12, Number 3 (1984), 887-897.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176346709

Digital Object Identifier
doi:10.1214/aos/1176346709

Mathematical Reviews number (MathSciNet)
MR751280

Zentralblatt MATH identifier
0557.62007

JSTOR
links.jstor.org

Subjects
Primary: 62C20: Minimax procedures
Secondary: 62G99: None of the above, but in this section 62F35: Robustness and adaptive procedures 62J99: None of the above, but in this section

Keywords
Consistency kernel estimates nearest neighbor estimates nonparametric regression smoothing splines Stein effect

Citation

Li, Ker-Chau; Hwang, Jiunn Tzon. The Data-Smoothing Aspect of Stein Estimates. Ann. Statist. 12 (1984), no. 3, 887--897. doi:10.1214/aos/1176346709. https://projecteuclid.org/euclid.aos/1176346709


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