Semiparametric modeling of the right-censored time-series based on different censorship solution techniques

In this paper, we employ the penalized spline method to estimate the components of a right-censored semiparametric time-series regression model with autoregressive errors. Because of the censoring, the parameters of such a model cannot be directly computed by ordinary statistical methods, and therefore, a transformation is required. In the context of this paper, we propose three different data transformation techniques, called Gaussian imputation (GI), k nearest neighbors (kNN) and Kaplan–Meier weights (KMW). Note that these data transformation methods, which are modified extensions of ordinary GI, kNN and KMW approximations, are used to adjust the censoring response variable in the setting of a time-series. In this sense, detailed Monte Carlo experiments and a real time-series data example are carried out to indicate the performances of the proposed approaches and to analyze the effects of different censoring levels and sample sizes. The obtained results reveal that the censored semiparametric time-series models based on kNN imputation often work better than those estimated by GI or KMW.