We consider the efficient estimation of the semiparametric additive
transformation model with current status data. A wide range of survival models
and econometric models can be incorporated into this general transformation
framework. We apply the B-spline approach to simultaneously estimate the linear
regression vector, the nondecreasing transformation function, and a set of
nonparametric regression functions. We show that the parametric estimate is
semiparametric efficient in the presence of multiple nonparametric nuisance
functions. An explicit consistent B-spline estimate of the asymptotic variance
is also provided. All nonparametric estimates are smooth, and shown to be
uniformly consistent and have faster than cubic rate of convergence.
Interestingly, we observe the convergence rate interfere phenomenon, i.e., the
convergence rates of B-spline estimators are all slowed down to equal the
slowest one. The constrained optimization is not required in our
implementation. Numerical results are used to illustrate the finite sample
performance of the proposed estimators.Comment: 32 pages, 5 figure
