Shrinkage Estimation and Bootstrap Confidence Interval for Scale Parameter of Laplace Distribution

Year 2023, Volume: 23 Issue: 4, 933 - 940, 31.08.2023

Şenay Özdemir , Meral Ebegil

https://doi.org/10.35414/akufemubid.1231989

Cited By: 1

Abstract

In this study, a biased estimator is proposed for the scale parameter of Laplace distribution. First, it is theoretically shown that the mean square error of the biased estimator is smaller than that of the maximum likelihood estimator. Then the maximum likelihood estimator is compared with the obtained biased estimator by means of a simulation study using the relative efficiency of these estimators. In addition, confidence intervals are constructed for the scale parameter of Laplace distribution with bootstrap method in order to compare them with each other in a different way.

Keywords

Bootstrap Confidence Interval, Laplace Distribution, Biased Estimation, Shrinkage Estimation

Laplace Dağılımının Ölçek Parametresi için Daraltıcı Tahmin ve Bootstrap Güven Aralığı

Abstract

Bu çalışmada, Laplace dağılımının ölçek parametresi için yanlı bir tahmin edici önerilmiştir. İlk olarak, yanlı tahmin edicinin hata kare ortalamasının, maksimum olabilirlik tahmin edicisininkinden daha küçük olduğu teorik olarak gösterilmiştir. Daha sonra maksimum olabilirlik tahmin edicisi ile elde edilen yanlı tahminci, bu tahmincilerin göreli etkinilikleri kullanılarak bir benzetim çalışması ile karşılaştırılmıştır. Ayrıca tahmin edicileri farklı bir açıdan karşılaştırmak için Laplace dağılımının ölçek parametresi için bootstrap yöntemi ile güven aralıkları oluşturulmuştur.

Keywords

Bootstrap Güven Aralığı, Laplace Dağılımı, Daraltıcı Tahmin, Yanlı Tahmin

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