Comparison of Confidence Interval Estimators: an Index Approach

In many statistical problems, several estimators are usually available for interval estimation of a parameter of interest, and hence, the selection of an appropriate estimator is important. The criterion for a good estimator is to have a high coverage probability close to the nominal level and a shorter interval length. However, these two concepts are in opposition to each other: high and low coverages are associated with longer and shorter interval lengths respectively. Some methods, such as bootstrap calibration, modify the nominal level to improve the coverage and thereby allow the selection of intervals based on interval lengths only. Nonetheless, these methods are computationally expensive. In this paper, we propose an index which offers an easy to compute approach of comparing confidence interval estimators based on a compromise between the coverage probability and the confidence interval length. We illustrate that the confidence interval index has range of values within the neighborhood of the range of the coverage probability, [0,1]. In addition, a good confidence interval estimator has an index value approaching 1; and a bad confidence interval has an index value approaching 0. A simulation study was conducted to assess the finite sample performance of the index. The proposed index is illustrated with a practical example from the literature