A note on confidence interval estimation for a linear function of binomial proportions

Zou, Guang Yong; Huang, Wenyi; Zhang, Xiaohe

doi:10.1016/j.csda.2008.09.033

Cited by 48 publications

(30 citation statements)

References 16 publications

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“…When K=2, there may be several objectives: the difference between the two proportions if  1 =1 and  2 =+1 (as in Agresti and Caffo, 2000); the sum of two proportions if  1 =+1 and  2 =+1 (as in Pham-Gia and Turkkan, 1994); the ratio  of two proportions if  1 = and  2 =+1 (as in Agresti, 2003); or a linear combination of two proportions with  1 <0 (as in Phillips, 2003). Cases with K>2 are historically rather less frequent, although in recent years they have received more and more attention due to their great practical interest (Newcombe, 2001;Price and Bonett, 2004;Schaarschmidt et al 2008;Tebbs and Roths, 2008;Agresti et al, 2008;Zou et al, 2009 andMartín et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

“…These authors concluded that the score method was the best, closely followed by a modification and generalization of the method proposed by Price and Bonett. Finally, Newcombe (2001) for K=4 and  i =0, and Zou et al (2009) for any value of K and of  i , suggest substituting the proportions of the Wald method with the boundaries of Wilson's CI (1927).…”

Section: Introductionmentioning

confidence: 99%

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The optimal method to make inferences about a linear combination of proportions

Andrés

Tejedor

Hernández

2012

Journal of Statistical Computation and Simulation

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Asymptotic inferences about a linear combination of K independent binomial proportions are very frequent in applied research. Nevertheless, until quite recently research had been focused almost exclusively on cases of K2 (particularly on cases of one proportion and the difference of two proportions). This article focuses on cases of K>2, which have recently begun to receive more attention due to their great practical interest.In order to make this inference, there are several procedures which have not been (which is a generalization of the Newcombe method). The article describes a new procedure (P0) based on the classic Peskun method, modifies the previous methods giving them continuity correction (methods S0c, W3c, N0c and P0c respectively) and, finally, a simulation is made to compare the eight aforementioned procedures (which are selected from a total of 32 possible methods). The conclusion reached is that S0c method is the best, although for very small samples (n i  10, i) the W3 method is better. The P0 method would be the optimal method if one needs a method which is almost never too liberal, but this entails using a method which is too conservative and which provides excessively wide confidence intervals. The W3 and P0 methods have the additional advantage of being very easy to apply.A free programme which allows the application of the S0 and S0c methods (which are the most complex) can be obtained at

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The optimal method to make inferences about a linear combination of proportions

Andrés

Tejedor

Hernández

2012

Journal of Statistical Computation and Simulation

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“…A confidence interval proposed by Zou et al [8], and referred to here as the ZHZ method, combines Wilson confidence intervals for each individual proportion. Let p k be the kth element of the 2m × 1 vector p, and c k be the kth element of the 2m × 1 vector c. A 100(1 − α)% ZHZ confidence interval for may be expressed as…”

Section: Introductionmentioning

confidence: 99%

“…The two methods were found to be similar in performance. [8] Some methods described by Tebbs and Roths [11] were not included in the simulation study of Grizzle et al [8] because of their poor worst-case coverage probabilities.…”

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confidence: 99%

A comparison of two varying coefficient meta-analysis methods for an average risk difference

Price

Bonett

2014

Journal of Statistical Computation and Simulation

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“…2 Zou et al (2009) have suggested an interval estimation for a linear function of binomial ratios. 3 Wencheko and Chipoyera (2009) have compared the MBBE estimator of the population variance and unbiased estimator when kurtosis coefficient is known. 2 They have studied boxplots of different sample sizes and estimators for Normal and Exponential distribution.…”

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confidence: 99%

Interval Estimation for Nonnormal Population Variance with Kurtosis Coeffificient Based on Trimmed Mean

Akyüz¹,

Gamgam²

2017

Turkiye Klinikleri J Biostat

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Objective: In random experiments, most analyses are based on interpretation of the difference between the means of experiment and control groups. Therefore, studying the variance of the experiment and control groups may also be useful in interpreting the analysis results. This study focuses on interval estimation based on minimum mean-squared error biased estimators for nonnormal population variance. It is aimed that kurtosis coefficient based on trimmed mean is used instead of sample kurtosis coefficient in this study. Material and Methods: With the simulation study in MATLAB R2009a, confidence intervals are obtained for the estimator which is obtained using both kurtosis coefficients. Coverage probabilities and average length widths of these confidence intervals were compared. Results: It was determined that the coverage probabilities of the estimator which was obtained by using the kurtosis coefficient based on trimmed mean is very close to the nominal confidence level in all sample sizes. It was also observed that the average length widths which were obtained by using the kurtosis coefficient based on trimmed mean are narrower than the average widths obtained with biased sample kurtosis coefficient. It was determined that the results are the same when Type I error is different. Using sample kurtosis coefficient for nonnormal populations resulted in obtaining low coverage probabilities. Conclusion: It will be appropriate to prefer interval estimations based on estimator obtained with kurtosis coefficient based on Trimmed Mean since it both provides high coverage probability and narrower confidence interval for nonnormal population variance.Keywords: Coverage probability; interval estimation; kurtosis coefficient; minimum mean-squared error; trimmed mean ÖZET Amaç: Rasgele deneylerde bir çok analiz deney ve kontrol gruplarının ortalamaları arasındaki farkın yorumlanmasına dayalıdır. Varyansların incelenmesi de analiz sonuçlarını yorumlamada faydalı olabilir. Bu çalışma normal dağılımlı olmayan yığın varyansı için minumum hata kareler ortalamalı yanlı tahmin ediciye dayalı aralık tahmini üzerinedir. Bu çalışmada örnek basıklık katsayısı yerine budanmış ortalamaya dayalı olarak elde edilen basıklık katsayısının kullanılması amaçlanmıştır. Gereç ve Yöntemler: MATLAB R2009a programında yapılan simülasyon çalışmasında her iki basıklık katsayısının kullanılması ile elde edilen tahmin ediciye dayalı güven aralıkları elde edilmiştir. Bu güven aralıklarına ait kapsama olasılıkları ve ortalama aralık genişlikleri karşılaştırılmıştır. Bulgular: Budanmış ortalamaya dayalı basıklık katsayısının kullanılması ile elde edilen tahmin edicinin güven aralığı kapsama olasılıklarının örnek hacimlerinin tamamında nominal güven düzeyine çok yakın olduğu belirlenmiştir. Aynı zamanda budanmış ortalamaya dayalı basıklık katsayısının kullanılması sonucunda elde edilen güven aralıklarının ortalama genişliklerinin, yanlı örnek basıklık katsayısı ile elde edilen güven aralıklarının ortalama genişliklerine göre daha dar olduğu görü...

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A note on confidence interval estimation for a linear function of binomial proportions

Cited by 48 publications

References 16 publications

The optimal method to make inferences about a linear combination of proportions

The optimal method to make inferences about a linear combination of proportions

A comparison of two varying coefficient meta-analysis methods for an average risk difference

Interval Estimation for Nonnormal Population Variance with Kurtosis Coeffificient Based on Trimmed Mean

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