Robust confidence regions for multinomial probabilities

ALIN A., Basu A.

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, vol.85, no.3, pp.538-551, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 85 Issue: 3
  • Publication Date: 2015
  • Doi Number: 10.1080/00949655.2013.828214
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.538-551
  • Keywords: 62H10, 62G10, 62G35, 62G09, multinomial parameters, confidence region, bootstrap, robustness, power-divergence test statistics, penalization, BOOTSTRAP, GOODNESS, TESTS, FIT, INTERVALS
  • Dokuz Eylül University Affiliated: Yes


Generally, confidence regions for the probabilities of a multinomial population are constructed based on the Pearson chi(2) statistic. Morales et al. (Bootstrap confidence regions in multinomial sampling. Appl Math Comput. 2004;155:295-315) considered the bootstrap and asymptotic confidence regions based on a broader family of test statistics known as power-divergence test statistics. In this study, we extend their work and propose penalized power-divergence test statistics-based confidence regions. We only consider small sample sizes where asymptotic properties fail and alternative methods are needed. Both bootstrap and asymptotic confidence regions are constructed. We consider the percentile and the bias corrected and accelerated bootstrap confidence regions. The latter confidence region has not been studied previously for the power-divergence statistics much less for the penalized ones. Designed simulation studies are carried out to calculate average coverage probabilities. Mean absolute deviation between actual and nominal coverage probabilities is used to compare the proposed confidence regions.