The Annals of Statistics

Semiparametric inference in a partial linear model

P. K. Bhattacharya and Peng-Liang Zhao

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Abstract

In a partial linear model, the dependence of a response variate Y on covariates (W, X$ is given by $$Y = W \beta + \eta(X) + \mathscr{E}$$ where $\mathscr{E}$ is independent of $(W, X)$ with densities g and f, respectively. In this paper an asymptotically efficient estimator of $\beta$ is constructed solely under mild smoothness assumptions on the unknown $\eta$, f and g, thereby removing the assumption of finite residual variance on which all least-squares-type estimators available in the literature are based.

Article information

Source
Ann. Statist., Volume 25, Number 1 (1997), 244-262.

Dates
First available in Project Euclid: 10 October 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1034276628

Digital Object Identifier
doi:10.1214/aos/1034276628

Mathematical Reviews number (MathSciNet)
MR1429924

Zentralblatt MATH identifier
0869.62050

Subjects
Primary: 62J99: None of the above, but in this section 62F12: Asymptotic properties of estimators
Secondary: 62G07: Density estimation

Keywords
Partial linear model semiparametric inference effective information efficient influence function bandwidth-matched $M$-estimator $M$-smoother

Citation

Bhattacharya, P. K.; Zhao, Peng-Liang. Semiparametric inference in a partial linear model. Ann. Statist. 25 (1997), no. 1, 244--262. doi:10.1214/aos/1034276628. https://projecteuclid.org/euclid.aos/1034276628


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References

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