A Parametric Test of Perfect Ranking in Balanced Ranked Set Sampling

Zamanzade, Ehsan; Arghami, Nasser Reza; Vock, Michael

doi:10.1080/03610926.2012.737495

Cited by 13 publications

(7 citation statements)

References 14 publications

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“…A number of tests of perfect rankings have been developed. Frey & Wang () and Zamanzade, Arghami, & Vock () proposed parametric tests, but most of the tests in the literature are nonparametric. For

j = 1, \dots, m

and

i = 1, \dots, n_{j}

, let

X_{false[j false] i}

be the i th independent value with rank j .…”

Section: Existing Tests Of Perfect Rankingsmentioning

confidence: 99%

Testing perfect rankings in ranked‐set sampling with binary data

Frey

Zhang

2017

Can J Statistics

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In ranked‐set sampling, the rankings may be either perfect or imperfect. Statistical procedures that assume perfect rankings tend to be more efficient than procedures that do not assume perfect rankings when perfect rankings actually hold, but may perform poorly if the rankings are imperfect. Several procedures have been developed for testing the null hypothesis of perfect rankings, but these procedures break down if the data are not continuous. In this article, we develop tests of perfect rankings that can be applied with binary data. Motivated by new theoretical results about how the success probabilities in the judgment strata differ under perfect and imperfect rankings, we develop a consistent test with a test statistic that is asymptotically normal. We find, however, that the test does not properly control the type I error rate with small samples. This motivates us to instead implement a bootstrap version of the test. This bootstrap test controls the type I error rate even with small sample sizes. Functions for implementing both tests using R are available in the Supplementary Material. The Canadian Journal of Statistics 45: 326–339; 2017 © 2017 Statistical Society of Canada

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j = 1, \dots, m

and

i = 1, \dots, n_{j}

, let

X_{false[j false] i}

be the i th independent value with rank j .…”

Section: Existing Tests Of Perfect Rankingsmentioning

confidence: 99%

Testing perfect rankings in ranked‐set sampling with binary data

Frey

Zhang

2017

Can J Statistics

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show abstract

“…The problem of estimating a distribution function has been considered by Stokes and Sager (1988), Kvam and Samaniego (1994), Duembgen and Zamanzade (2013). Frey et al (2007) and Li and Balakrishnan (2008) proposed some tests for assessing the assumption of prefect rankings, followed by Vock and Balakrishnan (2011), Zamanzade et al (2012), Frey and Wang (2013), and Zamanzade et al (2014).…”

Section: Introductionmentioning

confidence: 99%

Variance estimation in ranked set sampling using a concomitant variable

Zamanzade

Vock

2015

Statistics & Probability Letters

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“…As the ranking process in RSS is performed without obtaining precise values of the sample units, it may not to be accurate (perfect). Frey [3] and Li and Balakrishnan [5] proposed some nonparametric tests for assessing perfect ranking assumption which were followed by Vock and Balakrishnan [13], Zamanzade et al [14] and Zamanzade et al [15]. The problem of estimating the population mean and variance when RSS is applied by measuring a concomitant variable were discussed by Frey [4], Zamanzade and Mohammadi [17] and Zamanzade and Vock [16].…”

Section: Introductionmentioning

confidence: 99%