We consider nonparametric estimation of an accelerated failure-time model when the response variable is randomly censored on the right, and regressors are not mean independent of the error component. This dependence can arise, for instance, because of measurement error. We achieve identification and conduct estimation using a vector of instrumental variables. Censoring is independent of the response variable given the instruments. We consider settings in which regressors are continuously distributed. However, the instruments may or may not be continuous, and we show how various independence restrictions allow us to identify and estimate the unknown function of interest depending on the nature of instruments. We provide rates of convergence of our estimator and showcase its finite sample properties in simulations.
Jean-Pierre Florens acknowledges funding from the French National Research Agency (ANR) under the Investments for the Future program (Investissements d’Avenir, grant ANR-17-EURE-0010).
The authors would like to thank the Editor, Domenico Marinucci, the Associate Editor, and two anonymous referees whose comments and suggestions helped improve the manuscript.
"Nonparametric estimation of accelerated failure-time models with unobservable confounders and random censoring." Electron. J. Statist. 15 (2) 5333 - 5379, 2021. https://doi.org/10.1214/21-EJS1921