Local polynomial estimation for multi-response semiparametric regression models with right censored data

This study employs a multi-response semiparametric regression model designed for right-censored data, featuring an m-dimensional response variable. The aim is to estimate this model using modified local polynomial techniques, including its two specific cases: local linear and local constant estimators. The rationale for employing local-basis smoothers is their effectiveness in addressing issues with right-censored data through local fitting, particularly in multi-response scenarios. Additionally, synthetic data transformation is applied to incorporate censorship effects into the estimation process by replacing response variables with synthetic responses. To evaluate the performance of the proposed estimators, a comprehensive Monte Carlo simulation study is conducted, along with an analysis of a colon cancer dataset. Overall, the results indicate satisfactory model estimation, with the modified local constant estimator demonstrating a more balanced and stable performance compared to the other two estimators. The study also provides insights into the advantages and limitations of each modified estimator.