Right-Censored Time Series Modeling by Modified Semi-Parametric A-Spline Estimator

Abstract

This paper focuses on the adaptive spline (A-spline) fitting of the semiparametric regression model to time series data with right-censored observations. Typically, there are two main problems that need to be solved in such a case: dealing with censored data and obtaining a proper A-spline estimator for the components of the semiparametric model. The first problem is traditionally solved by the synthetic data approach based on the Kaplan–Meier estimator. In practice, although the synthetic data technique is one of the most widely used solutions for right-censored observations, the transformed data’s structure is distorted, especially for heavily censored datasets, due to the nature of the approach. In this paper, we introduced a modified semiparametric estimator based on the A-spline approach to overcome data irregularity with minimum information loss and to resolve the second problem described above. In addition, the semiparametric B-spline estimator was used as a benchmark method to gauge the success of the A-spline estimator. To this end, a detailed Monte Carlo simulation study and a real data sample were carried out to evaluate the performance of the proposed estimator and to make a practical comparison.

Regression with right-censored high-dimensional data: An application with different imputation techniques

“…Hence, partially observed responses are obtained with z i = min(y i , c i ). An algorithm for censoring procedure is provided by (Aydin et al, 2021).…”

Penalty and Shrinkage Strategies Based on Local Polynomials for Right-Censored Partially Linear Regression

“…Regarding the censoring data, the censoring variable is generated as independently of the initially observed variable . An algorithm is provided by [ 29 ]. Another important point for this study is the selection of the shrinkage parameters and the bandwidth parameter for the local polynomial approach for the introduced six estimators.…”

Nonparametric Statistical Inference with an Emphasis on Information-Theoretic Methods

“…In [7], the authors consider a semiparametric stationary time series model of the form Z t = x T t β + f (s t ) + ε t , where x t is a vector of random explanatory variables, s t is a temporal covariate, and ε t is an autoregressive process. Moreover, Z t is subject to random censoring from the right, and f is a linear combination of B-spline basis functions of order q with a corresponding vector of coefficients α.…”