Journal
ANNALS OF STATISTICS
Volume 33, Issue 5, Pages 2256-2290Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/009053605000000444
Keywords
current status data; empirical processes; nonparametric regression; semiparametric efficiency; splines; transformation models
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We consider partly linear transformation models applied to current status data. The unknown quantities are the transformation function, a linear regression parameter and a nonparametric regression effect. It is shown that the penalized MLE for the regression parameter is asymptotically normal and efficient and converges at the parametric rate, although the penalized MLE for the transformation function and nonparametric regression effect are only n(1/3) consistent. Inference for the regression parameter based on a block jackknife is investigated. We also study computational issues and demonstrate the proposed methodology with a simulation study. The transformation models and partly linear regression terms, coupled with new estimation and inference techniques, provide flexible alternatives to the Cox model for current status data analysis.
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