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2017 Parametric conditional variance estimation in location-scale models with censored data
Cédric Heuchenne, Géraldine Laurent
Electron. J. Statist. 11(1): 148-176 (2017). DOI: 10.1214/16-EJS1139

Abstract

Suppose the random vector $(X,Y)$ satisfies the regression model $Y=m(X)+\sigma (X)\varepsilon$, where $m(\cdot)=E(Y|\cdot),$ $\sigma^{2}(\cdot)=\mbox{Var}(Y|\cdot)$ belongs to some parametric class $\{\sigma _{\theta}(\cdot):\theta \in \Theta\}$ and $\varepsilon$ is independent of $X$. The response $Y$ is subject to random right censoring and the covariate $X$ is completely observed. A new estimation procedure is proposed for $\sigma _{\theta}(\cdot)$ when $m(\cdot)$ is unknown. It is based on nonlinear least squares estimation extended to conditional variance in the censored case. The consistency and asymptotic normality of the proposed estimator are established. The estimator is studied via simulations and an important application is devoted to fatigue life data analysis.

Citation

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Cédric Heuchenne. Géraldine Laurent. "Parametric conditional variance estimation in location-scale models with censored data." Electron. J. Statist. 11 (1) 148 - 176, 2017. https://doi.org/10.1214/16-EJS1139

Information

Received: 1 July 2015; Published: 2017
First available in Project Euclid: 1 February 2017

zbMATH: 1356.62172
MathSciNet: MR3604021
Digital Object Identifier: 10.1214/16-EJS1139

Subjects:
Primary: 62N01, 62N02
Secondary: 62N05

Rights: Copyright © 2017 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.11 • No. 1 • 2017
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