TWO LIKELIHOOD-BASED SEMIPARAMETRIC ESTIMATION METHODS FOR PANEL COUNT DATA WITH COVARIATES

By Jon A. Wellner, Ying Zhang. 2005

183 citations recorded by the source corpus.

We consider estimation in a particular semiparametric regression model for the mean of a counting process with \panel count" data. The basic model assumption is that the conditional mean function of the counting process is of the form EfN(t)jZg = exp(fl T Z)⁄0(t) where Z is a vector of covariates and ⁄0 is the baseline mean function. The \panel count" observation scheme involves observation of the counting processN for an individual at a random number K of random time points; both the number and the locations of these time points may difier across individuals. We study semiparametric maximum pseudo-likelihood and maximum likelihood estimators of the unknown parameters (fl0;⁄0) derived on the basis of a nonhomogeneous Poisson process assumption. The pseudo-likelihood estimator is fairly easy to compute, while the maximum likelihood estimator poses more challenges from the computational perspective. We study asymptotic properties of both estimators assuming that the proportional mean model holds, but dropping the Poisson process assumption used to derive the estimators. In particular we establish asymptotic normality for the estimators of the regression parameter fl0 under appropriate hypotheses. The results show that our estimation procedures are robust in the sense that the estimators converge to the truth regardless of the underlying counting process.

Subfields: Economics and Econometrics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1bf072eb6e7613d05448bdae9231fa0088ef16d9

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In Economics and Econometrics

1. Jian Huang
2. Minggen Lu
3. David Firth
4. Nancy Reid
5. Xiao Wang
6. Cristiano Varin
7. Donglin Zeng
8. Holger Rootz'en

In Statistics and Probability

1. David Firth
2. Jian Huang
3. Nancy Reid
4. Cristiano Varin
5. Minggen Lu
6. Ying Zhang
7. Donglin Zeng
8. Xiao Wang

Citations in the corpus

• Wiener processes with random effects for degradation data (2010, background): “2 are given in Appendix which are established similarly as in [23,24]).”
• Maximum likelihood estimation in semiparametric regression models with censored data (2007, background): “Wellner and Zhang (2005) studied proportional mean models for panel counts data with general interval censoring.”
• Semiparametric Estimation Methods for Panel Count Data Using Monotone B-Splines (2009, methodology): “One of the primary goals of this study was to determine the effect of treatment on suppressing the tumor recurrence; see, for example, Byar (1980), Wei, Lin, and Weissfeld (1989), Wellner and Zhang (2000, 2007), Sun and Wei (2000), and Lu, Zhang, and Huang (2007).”
• AN OVERVIEW OF COMPOSITE LIKELIHOOD METHODS (2011, methodology): “For example, Wellner and Zhang (2000, 2007) propose non-parametric and semi-parametric estimators for panel count data using an independence likelihood, and Andersen (2004) uses pairwise likelihood in the proportional hazards model.”
• Limit theorems for empirical processes of cluster functionals (2009, background): “In the important context of estimation for panel count data, two articles by Wellner and Zhang (2000, 2007) use uniform central limit theory for vectors of random lengths.”