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RISS 인기검색어
- 검색키워드
- 저자 : Frey Jesse (검색결과 5 건)
- 무료
- 기관 내 무료
- 유료
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An omnibus two-sample test for ranked-set sampling data
Jesse Frey,Yimin Zhang 한국통계학회 2019 Journal of the Korean Statistical Society Vol.48 No.1
We develop an omnibus two-sample test for ranked-set sampling (RSS) data. The test statistic is the conditional probability of seeing the observed sequence of ranks in the combined sample, given the observed sequences within the separate samples.Wecompare the test to existing tests under perfect rankings, finding that it can outperform existing tests in terms of power, particularly when the set size is large. The test does not maintain its level under imperfect rankings. However, one can create a permutation version of the test that is comparable in power to the basic test under perfect rankings and also maintains its level under imperfect rankings. Both tests extend naturally to judgment post-stratification, unbalanced RSS, and even RSS with multiple set sizes. Interestingly, the tests have no simple random sampling analog.
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Improved exact confidence intervals for a proportion using ranked-set sampling
Jesse Frey,Yimin Zhang 한국통계학회 2019 Journal of the Korean Statistical Society Vol.48 No.3
We develop new exact confidence intervals for a proportion using ranked-set sampling (RSS). The existing intervals arise from applying the method of Clopper and Pearson (1934) to the total number of successes. We improve on the existing intervals by using the method of Blaker (2000) and by replacing the total number of successes with the maximum likelihood estimator of the proportion. The new intervals outperform the existing intervals in terms of average expected length, and they are also good in an absolute sense, as they come within a few percentage points of a new theoretical bound on the average expected length. Like the existing intervals, the new intervals use a perfect rankings assumption. They are no longer exact under imperfect rankings, but provide coverage close to nominal for mild departures from perfect rankings.
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Robust confidence intervals for a proportion using ranked-set sampling
Frey Jesse,Zhang Yimin 한국통계학회 2021 Journal of the Korean Statistical Society Vol.50 No.4
We develop two new approximate confidence interval methods for estimating a population proportion using balanced ranked-set sampling (RSS). Unlike existing RSS-based methods, the new methods control the coverage probability well not just under perfect rankings, but also under imperfect rankings. One method uses a Wilson-type interval, and the other is based on making a mid-P adjustment to a Clopper–Pearson-type interval. Both methods rely on a new maximum-likelihood-based method for estimating the proportions in the judgment strata when the overall proportion is given, and both can be computed even for large sample sizes.
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Bootstrap confidence bands for the CDF using ranked-set sampling
Jesse Frey 한국통계학회 2014 Journal of the Korean Statistical Society Vol.43 No.3
In ranked-set sampling (RSS), a stratification by ranks is used to obtain a sample that tendsto be more informative than a simple random sample of the same size. Previous work hasshown that if the rankings are perfect, then one can use RSS to obtain Kolmogorov–Smirnovtype confidence bands for the CDF that are narrower than those obtained under simplerandom sampling. Herewedevelop Kolmogorov–Smirnov type confidence bands that workwell whether the rankings are perfect or not. These confidence bands are obtained byusing a smoothed bootstrap procedure that takes advantage of special features of RSS. Weshow through a simulation study that the coverage probabilities are close to nominal evenfor samples with just two or three observations. A new algorithm allows us to avoid thebootstrap simulation step when sample sizes are relatively small.
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Nonparametric maximum likelihood estimation of the distribution function using ranked-set sampling
Frey Jesse,Zhang Yimin 한국통계학회 2023 Journal of the Korean Statistical Society Vol.52 No.4
Kvam and Samaniego (J Am Stat Assoc 89: 526–537, 1994) derived an estimator that they billed as the nonparametric maximum likelihood estimator (MLE) of the distribution function based on a ranked-set sample. However, we show here that the likelihood used by Kvam and Samaniego (1994) is different from the probability of seeing the observed sample under perfect rankings. By appealing to results on order statistics from a discrete distribution, we write down a likelihood that matches the probability of seeing the observed sample. We maximize this likelihood by using the EM algorithm, and we show that the resulting MLE avoids certain unintuitive behavior exhibited by the Kvam and Samaniego (1994) estimator. We find that the new MLE outperforms both the Kvam and Samaniego (1994) estimator and the unbiased estimator due to Stokes and Sager (J Am Stat Assoc 83: 374– 381, 1988) in terms of integrated mean squared error under perfect rankings.
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