Linear regression with interval censored data
type: Item
instance of: scholarly article
title: Linear regression with interval censored data
zbMATH Open document ID: 0934.62036
author: Gang Li
author: Cun-Hui Zhang
published in: The Annals of Statistics
publication date: 1999-11-09T00:00:00Z
review text: Consider the linear model \[ Y_i=\beta^{\text{tr}}Z_i+\varepsilon_i,\quad 1\leq i\leq n, \] where \(Z_i\) are known covariate vectors and \(\beta\) is an unknown parameter vector. We are interested in estimating \(\beta\) from the current status data such that \[ X_i=(\delta_i,T_i,Z_i),\quad 1\leq i\leq n, \] are observed instead of the usual \((Y_i,Z_i)\), where \(\delta_i=I_{\{Y_i\leq T_i\}}\) for some censoring times \(T_i\). This observation scheme is also called the binary choice model and Case 1 interval censoring. We assume that the errors \(\{\varepsilon_i\}\) are independent of \(\{Z_i,T_i\}\) and are i.i.d. variables with a common distribution \(F(t)\). \(M\)-estimators for the regression coefficients are derived. Asymptotic consistency and normality of the \(M\)-estimators are obtained via an exponential inequality for \(U\)-statistics. Asymptotically efficient estimators are provided under mild conditions.
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62G20
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 1359558
zbMATH Keywords: U-statistics
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1024691244
OpenAlex ID: W1989331308
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DOI: 10.1214/AOS/1024691244
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description: scientific article; zbMATH DE number 1359558