The Annals of Statistics

Current status linear regression

Piet Groeneboom and Kim Hendrickx

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Abstract

We construct $\sqrt{n}$-consistent and asymptotically normal estimates for the finite dimensional regression parameter in the current status linear regression model, which do not require any smoothing device and are based on maximum likelihood estimates (MLEs) of the infinite dimensional parameter. We also construct estimates, again only based on these MLEs, which are arbitrarily close to efficient estimates, if the generalized Fisher information is finite. This type of efficiency is also derived under minimal conditions for estimates based on smooth nonmonotone plug-in estimates of the distribution function. Algorithms for computing the estimates and for selecting the bandwidth of the smooth estimates with a bootstrap method are provided. The connection with results in the econometric literature is also pointed out.

Article information

Source
Ann. Statist., Volume 46, Number 4 (2018), 1415-1444.

Dates
Received: June 2016
Revised: March 2017
First available in Project Euclid: 27 June 2018

Permanent link to this document
https://projecteuclid.org/euclid.aos/1530086421

Digital Object Identifier
doi:10.1214/17-AOS1589

Mathematical Reviews number (MathSciNet)
MR3819105

Zentralblatt MATH identifier
06936466

Subjects
Primary: 62G05: Estimation 62N01: Censored data models
Secondary: 62-04: Explicit machine computation and programs (not the theory of computation or programming)

Keywords
Current status linear regression MLE semiparametric model

Citation

Groeneboom, Piet; Hendrickx, Kim. Current status linear regression. Ann. Statist. 46 (2018), no. 4, 1415--1444. doi:10.1214/17-AOS1589. https://projecteuclid.org/euclid.aos/1530086421


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Supplemental materials

  • Supplement to “Current status linear regression”. We give the proofs of the results stated in Sections 3, 4 and 5 of the manuscript.