## The Annals of Statistics

### Estimation in a semiparametric partially linear errors-in-variables model

#### Abstract

We consider the partially linear model relating a response $Y$ to predictors ($X, T$) with mean function $X^{\top}\beta + g(T)$ when the $X$’s are measured with additive error. The semiparametric likelihood estimate of Severini and Staniswalis leads to biased estimates of both the parameter $\beta$ and the function $g(\cdot)$ when measurement error is ignored. We derive a simple modification of their estimator which is a semiparametric version of the usual parametric correction for attenuation. The resulting estimator of $\beta$ is shown to be consistent and its asymptotic distribution theory is derived. Consistent standard error estimates using sandwich-type ideas are also developed.

#### Article information

Source
Ann. Statist., Volume 27, Number 5 (1999), 1519-1535.

Dates
First available in Project Euclid: 23 September 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1017939140

Digital Object Identifier
doi:10.1214/aos/1017939140

Mathematical Reviews number (MathSciNet)
MR2001a:62094

Zentralblatt MATH identifier
0977.62036

#### Citation

Liang, Hua; Härdle, Wolfgang; Carroll, Raymond J. Estimation in a semiparametric partially linear errors-in-variables model. Ann. Statist. 27 (1999), no. 5, 1519--1535. doi:10.1214/aos/1017939140. https://projecteuclid.org/euclid.aos/1017939140

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• COLLEGE STATION, TEXAS 77843-3143 E-MAIL: carroll@stat.tamu.edu