New Bootstrap Methods for the Hypothesis Tests of the Population Mean in Ranked Set Sampling

Abstract

Ranked Set Sampling is an efficient technique when it is difficult to measure sampling units in respect to cost or time. Although this technique can be used for every sample sizes, the small sample sizes are preferred for better ranking. However, when the sample sizes are small, it is very difficult to obtain distribution of the statistic for the statistical inference such as hypothesis test. In this case, resampling techniques like bootstrap can be used to construct pseudo distribution of the statistics. In this study, the bootstrap methods for hypothesis test about population mean under ranked set sampling is given. A simulation study is also performed to examine the performance of these methods.

Keywords

• Ranked set sampling,Bootstrap,Powers of test,Monte Carlo simulation

Sıralı Küme Örneklemesinde Yığın Ortalamasına İlişkin Hipotez Testi İçin Yeni Bootstrap Metotları

Abstract

Sıralı küme örneklemesi, örnekleme birimlerini ölçmenin maliyet ve zaman bakımından zor olduğu durumda kullanılan etkin bir örnekleme tekniğidir. Bu teknik, her çapta örnek için kullanılabilir olmasına rağmen sıralama hatasını minimuma indirmek için küçük örnek çaplarında daha çok tercih edilir. Ancak, hipotez testi gibi istatistiksel çıkarsama yaparken küçük örnek çapı durumunda, istatistiğin kesin ya da asimptotik dağılımını elde etmek oldukça zordur. Bu durumda, istatistiğin yapay dağılımını elde etmek için Bootstrap gibi yeniden örnekleme teknikleri kullanılabilir. Bu çalışmada, sıralı küme örneklemesi altında yığın ortalamasına ilişkin hipotez testi için Bootstrap metotları verilmiştir. Ayrıca, verilen metotların performansını değerlendirmek için simülasyon çalışması yapılmıştır.

Keywords

• Sıralı küme örneklemesi,Bootstrap,Testin gücü,Monte Carlo simülasyonu

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