Web-based Supplementary Materials for \Smooth " Semiparametric Regression Analysis for Arbitrarily Censored Time-to-Event Data

In this appendix, we give more detail on the SNP density estimator, review work establishing its properties, and describe what is known about its performance when it has been embedded in various complex statistical models. We refer the reader to the references cited, especially Gallant and Nychka (1987) and Fenton and Gallant (1996, 1996b), for technical details and further developments. The SNP density estimator is a truncation (or sieve) estimator based on a Hermite series expansion and was originally introduced by Gallant and Nychka (1987) in the context of representing the nonparametric part of nonlinear structural models popular in econometric analysis. These models can be rather complicated and would ordinarily also include a ¯nite-dimensional parametric component, as in the semiparametric time-to-event regression models we consider. Since its introduction, the SNP has been used in numerous applications with great success, where it has been embedded in various complex statistical models involving possibly numerous additional parameters of interest. These include in econometric models for stock volatility (Gallant, Hansen, and Tauchen, 1990), as a model for a bivariate distribution in binary choice models for labor-force participation (Gabler, Laisney, and Lechner, 1993)