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Some Shrinkage estimators based on median ranked set sampling.

Meral Ebegil1, Yaprak Arzu Özdemir1, Fikri Gökpinar1

  • 1Faculty of Science Department of Statistics, Gazi University, Ankara, Turkey.

Journal of Applied Statistics
|June 16, 2022
PubMed
Summary

This study introduces shrinkage estimators for multicollinearity using median ranked set sampling. The Ridge estimator is effective for moderate collinearity, while the Liu-type estimator excels with increasing collinearity.

Keywords:
Liu-type estimatorMedian ranked set samplingMonte Carlo simulationRidge regressionmulticollinearity

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Area of Science:

  • Statistics
  • Econometrics

Background:

  • Multicollinearity poses challenges in multiple regression analysis.
  • Ranked set sampling offers an alternative data collection method.
  • Shrinkage estimators can mitigate multicollinearity effects.

Purpose of the Study:

  • To investigate shrinkage estimators in the presence of multicollinearity using median ranked set sampling.
  • To adapt Ridge and Liu-type estimators for median ranked set samples.
  • To compare the efficiency of these estimators against others based on ranked set samples.

Main Methods:

  • Construction of a multiple regression model utilizing median ranked set sampling.
  • Adaptation of Ridge and Liu-type estimators to the developed model.
  • Performance evaluation through a comprehensive simulation study with varying parameters (sample size, correlation, error variance) and ranking qualities (perfect/imperfect).

Main Results:

  • The Ridge estimator with median ranked set sample outperforms others under moderate collinearity.
  • The Liu-type estimator with median ranked set sample shows superior performance as collinearity intensifies.
  • The efficiency threshold where the Ridge estimator is more effective than the Liu-type estimator (collinearity < 0.95) is influenced by sample size and the number of explanatory variables.

Conclusions:

  • Median ranked set sampling provides a viable framework for applying shrinkage estimators in multicollinear conditions.
  • The choice between Ridge and Liu-type estimators depends on the degree of collinearity.
  • The study highlights the practical implications of collinearity on estimator performance, further illustrated by a real data example.