TY - JOUR
T1 - A comparison of some confidence intervals for a binomial proportion based on a shrinkage estimator
AU - Almendra-Arao, Félix
AU - Reyes-Cervantes, Hortensia
AU - Morales-Cortés, Marcos
N1 - Publisher Copyright:
© 2023 the author(s), published by De Gruyter.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - Confidence intervals are valuable tools in statistical practice for estimating binomial proportions, with the most well-known being the Wald and Clopper-Pearson intervals. However, it is known that these intervals perform poorly in terms of coverage probability and expected mean length, leading to the proposal of alternative intervals in the literature, although these may also have deficiencies. In this work, we investigate the performance of several of these confidence intervals using the parametric family p ^ c = X + c/n + 2c with c ≥ 0 to estimate the parameter p p. Rather than using the confidence intervals approach, this analysis is done from the hypothesis tests approach. Our primary goal with this work is to identify values of c that result in better-performing tests and to establish an optimal procedure.
AB - Confidence intervals are valuable tools in statistical practice for estimating binomial proportions, with the most well-known being the Wald and Clopper-Pearson intervals. However, it is known that these intervals perform poorly in terms of coverage probability and expected mean length, leading to the proposal of alternative intervals in the literature, although these may also have deficiencies. In this work, we investigate the performance of several of these confidence intervals using the parametric family p ^ c = X + c/n + 2c with c ≥ 0 to estimate the parameter p p. Rather than using the confidence intervals approach, this analysis is done from the hypothesis tests approach. Our primary goal with this work is to identify values of c that result in better-performing tests and to establish an optimal procedure.
KW - binomial proportion
KW - confidence interval
KW - coverage probability
KW - shrinkage estimator
UR - http://www.scopus.com/inward/record.url?scp=85161337300&partnerID=8YFLogxK
U2 - 10.1515/math-2022-0588
DO - 10.1515/math-2022-0588
M3 - Artículo
AN - SCOPUS:85161337300
SN - 2391-5455
VL - 21
JO - Open Mathematics
JF - Open Mathematics
IS - 1
M1 - 20220588
ER -