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2015 Estimating the error distribution in semiparametric transformation models
Cédric Heuchenne, Rawane Samb, Ingrid Van Keilegom
Electron. J. Statist. 9(2): 2391-2419 (2015). DOI: 10.1214/15-EJS1057

Abstract

In this paper we consider the semiparametric transformation model $\Lambda_{\theta_{o}}(Y)=m(X)+\varepsilon$, where $\theta_{o}$ is an unknown finite dimensional parameter, the function $m(\cdot)=\mathbb{E}(\Lambda_{\theta_{o}}(Y)|X=\cdot)$ is “smooth”, but otherwise unknown, and the covariate $X$ is independent of the error $\varepsilon$. An estimator of the distribution function of $\varepsilon$ is investigated and its weak convergence is proved. The proposed estimator depends on a profile likelihood estimator of $\theta_{o}$ and a nonparametric kernel estimator of $m$. We also evaluate the practical performance of our estimator in a simulation study for several models and sample sizes. Finally, the method is applied to a data set on the scattering of sunlight in the atmosphere.

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Cédric Heuchenne. Rawane Samb. Ingrid Van Keilegom. "Estimating the error distribution in semiparametric transformation models." Electron. J. Statist. 9 (2) 2391 - 2419, 2015. https://doi.org/10.1214/15-EJS1057

Information

Received: 1 October 2014; Published: 2015
First available in Project Euclid: 29 October 2015

zbMATH: 1327.62257
MathSciNet: MR3417187
Digital Object Identifier: 10.1214/15-EJS1057

Subjects:
Primary: 62G08
Secondary: 62E20

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

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