The Novel HEWMA Exponential Type Mean Estimator under Ranked Set Sampling

Abstract

Introduction This study introduces a novel HEWMA-based memory-type exponential estimator for Ranked Set Sampling (RSS). The proposed estimator combines HEWMA control chart statistics with the exponential ratio estimator to enhance efficiency. By incorporating control chart statistics, memory-type estimators improve estimation accuracy by using both the current sample's mean and past mean(s), if available. This method is particularly beneficial for time-dependent repeated survey data or data collected from the same population at different time points. Material and Methods The proposed estimator's performance is evaluated through simulation studies using synthetic datasets, which simulate various scenarios with different correlation coefficients. An empirical study is also conducted using real-world data with a distinct structure. The evaluation focuses on the estimator's efficiency, considering factors such as sample size, correlation, and the number of past means incorporated. Results The simulation results demonstrate that incorporating at least one past sample mean value significantly enhances efficiency. Moreover, the estimator's effectiveness improves as both the correlation between samples and the number of old means (T) increase. The weight parameters of the HEWMA estimator play a critical role in determining its performance, with optimal results observed at low to medium correlation levels. The estimator consistently outperforms the existing alternatives in the real data analysis. Discussion The proposed HEWMA-based memory-type exponential estimator offers a more efficient alternative to the EWMA-type ratio estimator in the RSS method. The findings highlight the importance of selecting appropriate HEWMA weight parameters based on sample size and correlation. This approach substantially improves estimation accuracy, especially in time-dependent and longitudinal data scenarios. The proposed estimator performs particularly well under low to medium correlation conditions, and its applicability to real-world data further supports its practical utility.

Keywords

• Ranked set sampling
• HEWMA
• memory type
• estimator
• simulation

Supporting Institution

N/A

Ethical Statement

N/A

Sıralı Küme Örneklemesi Altında Yeni HEWMA Üstel Ortalama Tahmin Edici

Abstract

Giriş Bu çalışma, Sıralı Küme Örneklemesi (SKÖ) için yeni bir HEWMA tabanlı bellek tipi üstel tahmin ediciyi tanıtmaktadır. Önerilen tahmin edici, verimliliği artırmak için HEWMA kontrol çizelgesi istatistiklerini üstel oran tahmin edicisiyle birleştirir. Kontrol çizelgesi istatistiklerini dahil ederek, bellek tipi tahmin ediciler, mevcut örneklem ortalamasını ve varsa geçmiş ortalamaları kullanarak tahmin doğruluğunu artırır. Bu yöntem, özellikle zamana bağlı tekrarlanan anket verileri veya aynı popülasyondan farklı zaman noktalarında toplanan veriler için faydalıdır. Malzeme ve Yöntemler Önerilen tahmin edicinin performansı, farklı korelasyon katsayılarına sahip çeşitli senaryoları simüle eden sentetik veri kümeleri kullanılarak simülasyon çalışmaları yoluyla değerlendirilir. Ayrıca, belirgin bir yapıya sahip gerçek dünya verileri kullanılarak bir ampirik çalışma yürütülür. Değerlendirme, örneklem büyüklüğü, korelasyon ve dahil edilen geçmiş ortalamaların sayısı gibi faktörleri göz önünde bulundurarak tahmin edicinin verimliliğine odaklanır. Sonuçlar Simülasyon sonuçları, en az bir geçmiş örnek ortalama değerinin dahil edilmesinin verimliliği önemli ölçüde artırdığını göstermektedir. Dahası, tahmincinin etkinliği hem örnekler arasındaki korelasyon hem de eski ortalamaların (T) sayısı arttıkça iyileşmektedir. HEWMA tahmincisinin ağırlık parametreleri, performansını belirlemede kritik bir rol oynamaktadır ve düşük ila orta korelasyon seviyelerinde en iyi sonuçlar gözlemlenmektedir. Önerilen tahmin edici, gerçek veri analizinde mevcut alternatiflerden sürekli olarak daha iyi performans göstermektedir. Tartışma Önerilen HEWMA tabanlı bellek tipi üstel tahminci, SKÖ yönteminde EWMA tipi oran tahmincisine göre daha verimli bir alternatif sunmaktadır. Bulgular, örneklem büyüklüğü ve korelasyona dayalı uygun HEWMA ağırlık parametrelerinin seçilmesinin önemini vurgulamaktadır. Bu yaklaşım, özellikle zamana bağlı ve uzunlamasına veri senaryolarında tahmin doğruluğunu önemli ölçüde artırmaktadır. Önerilen tahminci, özellikle düşük ila orta korelasyon koşulları altında iyi performans göstermektedir ve gerçek dünya verilerine uygulanabilirliği, pratik faydasını daha da desteklemektedir.

Keywords

• Sıralı küme örneklemesi
• HEWMA
• bellek tipi
• tahmin edici
• simülasyon

Supporting Institution

N/A

Ethical Statement

N/A

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