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Modified Local Linear Estimators in Partially Linear Additive Models with Right-Censored Data Based on Different

Ersin Yılmaz1, Dursun Aydın1, S Ejaz Ahmed2

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Summary

This study presents a modified local linear estimator for right-censored partially linear additive models. The new method offers a non-iterative solution, performing well with Kaplan-Meier weights and kNN imputation.

Keywords:
kNN imputationlocal linear regressionpartially linear additive modelsright-censored datasynthetic data

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Partially linear additive models (PLAM) provide a flexible framework for statistical modeling.
  • Right-censored data is common in survival analysis and requires specialized estimation techniques.
  • Existing methods for censored PLAM can be complex or limited in scope.

Purpose of the Study:

  • To introduce a modified local linear estimator (LLR) for partially linear additive models (PLAM) with right-censored response variables.
  • To develop a non-iterative estimation procedure for censored PLAM.
  • To compare the performance of different methods for handling censored data within PLAM.

Main Methods:

  • Utilized a modified local linear regression (LLR) approach.
  • Employed a modified backfitting algorithm for non-iterative estimation.
  • Investigated three methods for handling right-censorship: synthetic data transformation (ST), Kaplan-Meier weights (KMW), and kNN imputation (kNNI).

Main Results:

  • The modified LLR provides a non-iterative solution for right-censored PLAM.
  • Asymptotic properties of the estimators using ST and KMW were derived.
  • Simulation studies and a real data example demonstrated the effectiveness of LLR, particularly with KMW and kNNI.

Conclusions:

  • The proposed modified local linear estimator is a viable and efficient method for analyzing right-censored partially linear additive models.
  • Kaplan-Meier weights and kNN imputation are effective strategies for addressing censoring in this context.
  • The LLR approach offers practical advantages for real-world data analysis where censoring is present.