Electronic Journal of Statistics

Parametric conditional variance estimation in location-scale models with censored data

Cédric Heuchenne and Géraldine Laurent

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 11, Number 1 (2017), 148-176.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1485939611

Digital Object Identifier
doi:10.1214/16-EJS1139

Mathematical Reviews number (MathSciNet)
MR3604021

Zentralblatt MATH identifier
1356.62172

Subjects
Primary: 62N01: Censored data models 62N02: Estimation
Secondary: 62N05: Reliability and life testing [See also 90B25]

Keywords
bandwidth bootstrap kernel method least squares estimation nonparametric regression right censoring survival analysis

Citation

Heuchenne, Cédric; Laurent, Géraldine. Parametric conditional variance estimation in location-scale models with censored data. Electron. J. Statist. 11 (2017), no. 1, 148--176. doi:10.1214/16-EJS1139. https://projecteuclid.org/euclid.ejs/1485939611


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