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March, 1988 Convergence Rates for Parametric Components in a Partly Linear Model
Hung Chen
Ann. Statist. 16(1): 136-146 (March, 1988). DOI: 10.1214/aos/1176350695


Consider the regression model $Y_i = X'_i\beta + g(t_i) + e_i$ for $i = 1, \cdots, n$. Here $g$ is an unknown Holder continuous function of known order $p$ in $R, \beta$ is a $k \times 1$ parameter vector to be estimated and $e_i$ is an unobserved disturbance. Such a model is often encountered in situations in which there is little real knowledge about the nature of $g$. A piecewise polynomial $g_n$ is proposed to approximate $g$. The least-squares estimator $\hat\beta$ is obtained based on the model $Y_i = X'_i\beta + g_n(t_i) + e_i$. It is shown that $\hat\beta$ can achieve the usual parametric rates $n^{-1/2}$ with the smallest possible asymptotic variance for the case that $X$ and $T$ are correlated.


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Hung Chen. "Convergence Rates for Parametric Components in a Partly Linear Model." Ann. Statist. 16 (1) 136 - 146, March, 1988.


Published: March, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0637.62067
MathSciNet: MR924861
Digital Object Identifier: 10.1214/aos/1176350695

Primary: 62J05
Secondary: 62G99, 62J10

Rights: Copyright © 1988 Institute of Mathematical Statistics


Vol.16 • No. 1 • March, 1988
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