In some semiparametric survival models with time dependent coefficients, a closed-form solution for coefficients estimates does not exist. Therefore, they have to be estimated by using approximate numerical methods. Due to the complicated forms of such estimators, it is too hard to extract their sampling distributions. In such cases, one usually uses the asymptotic theory to evaluate properties of the estimators. In this paper, first the model is introduced and a method is proposed, by using the Taylor expansion and kernel methods, to estimate the model. Then, the consistency and asymptotic normality of the estimators are established. The performance of the model and estimating procedure are evaluated by a heavy simulation study as well. Finally, the proposed model is applied on a real data set on heart disease patients in one of the Mashhad hospitals.

In this paper, we introduce a two-step procedure, in the context of high dimensional additive models, to identify nonzero linear and nonlinear components. We first develop a sure independence screening procedure based on the distance correlation between predictors and marginal distribution function of the response variable to reduce the dimensionality of the feature space to a moderate scale. Then a double penalization based procedure is applied to identify nonzero and linear components, simultaneously. We conduct extensive simulation experiments and a real data analysis to evaluate the numerical performance of the proposed method.