Semiparametric Additive Transformation Model under Current Status Data

TL;DR

This paper develops an efficient semiparametric estimation method for additive transformation models with current status data, using B-splines to estimate multiple functions simultaneously, with proven efficiency and practical performance.

Contribution

It introduces a B-spline based estimation framework for semiparametric additive transformation models that achieves efficiency and handles multiple nonparametric components without constrained optimization.

Findings

B-spline estimators are uniformly consistent with faster than cubic convergence rates.

The convergence rate interference phenomenon causes all estimators to slow down to the slowest rate.

Numerical results demonstrate good finite sample performance of the proposed estimators.

Abstract

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.