Penalized log-likelihood estimation for partly linear transformation models with current status data

Details Penalized log-likelihood estimation for partly linear transformation models with current status data Penalized log-likelihood estimation for partly linear transformation models with current status data

2006-02-11

arxiv.org/abs/math/0602243v1

Annals of Statistics 2005, Vol. 33, No. 5, 2256-2290

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000444 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053605000000444

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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