Rescaled bootstrap confidence intervals for the population variance in the presence of outliers or spikes in the distribution of a variable of interest

Abstract

Confidence intervals for the population variance in the presence of outliers or spikes in the distribution of a variable of interest are topics that have not been investigated in depth previously. Results derived from a first Monte Carlo simulation study reveal the limitations of the customary confidence interval for the population variance when the underlying assumptions are violated, and the use of alternative confidence intervals is thus justified. We suggest confidence intervals based on the rescaled bootstrap method for many reasons. First, this is a simple technique that can be easily applied in practice. Second, it is free of probabilistic distributions. Finally, it can be easily applied to the cases of finite populations and samples selected from complex sampling designs. Results derived from a second Monte Carlo simulation study indicate that the suggested confidence intervals have desirable coverage rates with smaller average widths. Accordingly, an advantage of the suggested confidence intervals is that they offer a good compromise between simplicity and desirable properties. The various simulation studies are based on different scenarios that may arise in practice, such as the presence of outliers or spikes, and the fact that the underlying assumptions of the customary confidence interval are violated.