We consider the efficient estimation of the semiparametric additivetransformation model with current status data. A wide range of survival modelsand econometric models can be incorporated into this general transformationframework. We apply the B-spline approach to simultaneously estimate the linearregression vector, the nondecreasing transformation function, and a set ofnonparametric regression functions. We show that the parametric estimate issemiparametric efficient in the presence of multiple nonparametric nuisancefunctions. An explicit consistent B-spline estimate of the asymptotic varianceis also provided. All nonparametric estimates are smooth, and shown to beuniformly consistent and have faster than cubic rate of convergence.Interestingly, we observe the convergence rate interfere phenomenon, i.e., theconvergence rates of B-spline estimators are all slowed down to equal theslowest one. The constrained optimization is not required in ourimplementation. Numerical results are used to illustrate the finite sampleperformance of the proposed estimators.
展开▼
