Bernoulli

  • Bernoulli
  • Volume 11, Number 5 (2005), 863-892.

An asymptotic theory for the nonparametric maximum likelihood estimator in the Cox gene model

I-Shou Chang, Chao Agnes Hsiung, Mei-Chuan Wang, and Chi-Chung Wen

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Abstract

The Cox model with a gene effect for age at onset was introduced and studied by Li, Thompson and Wijsman. We study the nonparametric maximum likelihood estimation of the gene effect and the regression coefficient in this model. We indicate conditions under which the parameters are identifiable and the nonparametric maximum likelihood estimate is consistent and asymptotically normal. We also apply the theory of observed profile information to obtain a consistent estimate of the asymptotic variance. Besides providing theoretical support for Li et al., our work provides an alternative approach to the numerical methods in this model.

Article information

Source
Bernoulli, Volume 11, Number 5 (2005), 863-892.

Dates
First available in Project Euclid: 23 October 2005

Permanent link to this document
https://projecteuclid.org/euclid.bj/1130077598

Digital Object Identifier
doi:10.3150/bj/1130077598

Mathematical Reviews number (MathSciNet)
MR2172845

Zentralblatt MATH identifier
1085.62052

Keywords
age at onset asymptotic normality Cox gene model discrete frailty model identifiability nonparametric maximum likelihood estimate profile likelihood information

Citation

Chang, I-Shou; Agnes Hsiung, Chao; Wang, Mei-Chuan; Wen, Chi-Chung. An asymptotic theory for the nonparametric maximum likelihood estimator in the Cox gene model. Bernoulli 11 (2005), no. 5, 863--892. doi:10.3150/bj/1130077598. https://projecteuclid.org/euclid.bj/1130077598


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