Robustness of The Confidence Interval for At-Risk-Of-Poverty-Rate
Languages of publication
Zieliński (2009) constructed a nonparametric interval for At-Risk-of-Poverty-Rate. It appeared that the confidence level of the interval depends on the underlying distribution of the income. For some distributions (e.g. lognormal, gamma, Pareto) the confidence level may be smaller than the nominal one. The question is, what is the largest deviance from the nominal level? In the paper, a more general problem is considered, i.e. the problem of robustness of the confidence level of the confidence interval for binomial probability. The worst distribution is derived as well as the smallest true confidence level is calculated. Some asymptotic remarks (sample size tends to infinity) are also given.
- CLOPPER C. J., PEARSON E. S. (1934), The Use of Confidence or Fiducial Limits Illustrated in the Case of the Binomial, Biometrika, 26, 404-413.
- ZIELIŃSKI R. (2006) Exact distribution of the natural ARPR estimator in small samples from infinite populations, Statistics In Transition, 7, 881-888.
- ZIELIŃSKI W. (2009), A nonparametric confidence interval for At-Risk-of-Poverty-Rate, Statistics in Transition new series, 10, 437-444.
Publication order reference