The Annals of Statistics

Efficient Estimates in Semiparametric Additive Regression Models with Unknown Error Distribution

Jack Cuzick

Full-text: Open access

Abstract

Several authors have shown how to efficiently estimate $\beta$ in the semiparametric additive model $y = x'\beta + g(t) + \text{error}$, $g(t)$ smooth but unknown when the error distribution is normal. However, the general theory suggests that efficient estimation should be possible for general error distributions with finite Fisher information even when the error distribution is unknown. In this note we construct a sequence of estimators which achieves this goal under technical assumptions.

Article information

Source
Ann. Statist., Volume 20, Number 2 (1992), 1129-1136.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348675

Digital Object Identifier
doi:10.1214/aos/1176348675

Mathematical Reviews number (MathSciNet)
MR1165611

Zentralblatt MATH identifier
0746.62037

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62J05: Linear regression 62F35: Robustness and adaptive procedures

Keywords
Semiparametric regression additive models linear models Hajek-Le Cam lower bound efficient estimators

Citation

Cuzick, Jack. Efficient Estimates in Semiparametric Additive Regression Models with Unknown Error Distribution. Ann. Statist. 20 (1992), no. 2, 1129--1136. doi:10.1214/aos/1176348675. https://projecteuclid.org/euclid.aos/1176348675


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