Shrinkage Estimators for the Location Parameter of the Normal Distribution in Median Ranked Set Sampling

Abstract

Unbiased estimators of the population parameters are often used to make an inference about the population. In cases where unbiased estimators have large variance, biased estimators such as shrinkage estimators may be preferred. In this study, shrinkage estimators of the location parameter of the normal distribution were obtained under ranked set sampling and median ranked set sampling. In addition, mean square errors of shrinkage estimators were obtained theoretically under ranked set sampling and median ranked set sampling. In order to examine the efficiency of the estimators, the mean square errors were calculated under different conditions using Monte Carlo simulation study. According to the results, it was observed that the shrinkage estimators obtained under median ranked set sampling were more efficient than the shrinkage estimators obtained under ranked set sampling and simple random sampling.

Keywords

• Ranked Set Sampling
• Median Ranked Set Sampling
• Mean Square Error
• Shrinkage Estimator

Medyan Sıralı Küme Örneklemesinde Normal Dağılımın Konum Parametresi İçin Shrinkage Tahmin Edicileri

Abstract

Yığına ilişkin bir çıkarsama yapabilmek için genellikle yığın parametrelerinin sapmasız tahmin edicileri kullanılır. Sapmasız tahmin edicilerin büyük varyansa sahip olmaları durumunda, shrinkage tahmin edicileri gibi sapmalı tahmin ediciler tercih edilebilir. Bu çalışmada, normal dağılımın konum parametresi için shrinkage tahmin edicileri, sıralı küme örneklemesi ve medyan sıralı küme örneklemesi kullanılarak elde edilmiştir. Ayrıca sıralı küme örneklemesi ve medyan sıralı küme örneklemesi altında elde edilen shrinkage tahmin edicilerinin ortalama hata kareleri teorik olarak elde edilmiştir. Önerilen tahmin edicilerin etkinliklerini incelemek amacıyla farklı durumlar altında Monte Carlo simülasyon çalışması ile ortalama hata kareleri hesaplanmıştır. Elde edilen sonuçlara göre, medyan sıralı küme örneklemesi kullanılarak elde edilen shrinkage tahmin edicilerinin sıralı küme örneklemesi ve basit tesadüfi örnekleme altında elde edilen shrinkage tahmin edicilerinden daha etkin olduğu gözlemlenmiştir.

Keywords

• Sıralı küme örneklemesi
• Medyan sıralı küme örneklemesi
• Ortalama hata kare
• Shrinkage tahmin edicisi
• Ranked Set Sampling
• Median Ranked Set Sampling
• Mean Square Error
• Shrinkage Estimator

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