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Nonparametric estimation of mean residual lifetime in ranked set sampling with a concomitant variable.

Ehsan Zamanzade1,2, M Mahdizadeh3, Hani M Samawi4

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Summary

This study introduces new methods for estimating mean residual lifetime (MRL) using ranked set sampling and a concomitant variable. These novel regression-based estimators outperform standard methods when ranking quality is good.

Keywords:
62D0562G05Judgment rankingMonte Carlo simulationnonparametric regressionranked set samplingrelative efficiency

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Area of Science:

  • Statistics
  • Survival Analysis
  • Reliability Engineering

Background:

  • The mean residual lifetime (MRL) is crucial for predicting future lifespan after a certain time.
  • MRL estimation is vital in fields like reliability and survival analysis.
  • Existing MRL estimation methods often rely on simple random sampling.

Purpose of the Study:

  • To develop and evaluate new MRL estimators using ranked set sampling (RSS).
  • To leverage concomitant variable information for improved MRL estimation.
  • To compare novel RSS-based MRL estimators against standard methods.

Main Methods:

  • Utilized ranked set sampling (RSS) with a concomitant variable.
  • Developed several MRL estimators employing regression techniques.
  • Conducted comparisons using Monte Carlo simulations and a real-world dataset (SEER Program).

Main Results:

  • The proposed MRL estimators based on RSS and regression showed superior performance.
  • Effectiveness of the new methods is contingent on good ranking quality in RSS.
  • The developed estimators provide more accurate MRL estimates than standard methods in simple random sampling.

Conclusions:

  • Regression-based MRL estimators in ranked set sampling offer significant advantages.
  • The choice of sampling method and ranking quality critically impacts MRL estimation accuracy.
  • This research provides enhanced tools for MRL estimation in survival and reliability analyses.