Confidence intervals for the parameter of the scaled-uniform model

The scaled-uniform model has been lately considered to illustrate problems in frequentist point estimation arising when the minimal sufficient statistic is not complete. Here we consider the problem of interval estimation and derive pivotal quantities based on a series of point estimators proposed in the literature. We compare the resulting intervals of given confidence level in terms of expected lengths. Pivotal quantities, confidence intervals and expected lengths are all computed using simulations implemented with R (code is available). Numerical results suggest that the maximum likelihood estimator, regardless of its inefficiency, yields confidence intervals that outperform the other available sets of the same level.