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August 1998 Cumulative regression function tests for regression models for longitudinal data
Thomas H. Scheike, Mei-Jie Zhang
Ann. Statist. 26(4): 1328-1355 (August 1998). DOI: 10.1214/aos/1024691245


The longitudinal regression model $Y_{i,j} = m(V_\tau_{i,j}^i) + \varepsilon_{i,j}$ where $Y_{i,j}$, is the $j$th measurement of the $i$th subject at random time $\tau_{i,j}$, $m$ is the regression function, $V_\tau_{i, j}$ is a predictable covariate process observed at time $\tau_{i,j}$ and $\varepsilon_{i,j}$ is noise, often provides an adequate framework for modeling and comparing groups of data. The proposed longitudinal regression model is based on marked point process theory, and allows a quite general dependency structure among the observations.

In this paper we find the asymptotic distribution of the cumulative regression function (CRF), and present a nonparametric test to compare the regression functions for two groups of longitudinal data. The proposed test, denoted the CRF test, is based on the cumulative regression function (CRF) and is the regression equivalent of the log-rank test in survival analysis. We show as a special case that the CRF test is valid for groups of independent identically distributed regression data. Apart from the CRF test, we also consider a maximal deviation statistic that may be used when the CRF test is inefficient.


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Thomas H. Scheike. Mei-Jie Zhang. "Cumulative regression function tests for regression models for longitudinal data." Ann. Statist. 26 (4) 1328 - 1355, August 1998.


Published: August 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0930.62049
MathSciNet: MR1647665
Digital Object Identifier: 10.1214/aos/1024691245

Primary: 62M10
Secondary: 62G07 , 62G10 , 62G20

Keywords: Conditional regression models , cumulative regression function , longitudinal data , marked point process , maximal deviation statistic , Nonparametric test , one-sample test , two-sample test

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.26 • No. 4 • August 1998
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