Non-Asymptotic Confidence Sets for Circular Means

Abstract

The mean of data on the unit circle is defined as the minimizer of the average squared Euclidean distance to the data. Based on Hoeffding’s mass concentration inequalities, non-asymptotic confidence sets for circular means are constructed which are universal in the sense that they require no distributional assumptions. These are then compared with asymptotic confidence sets in simulations and for a real data set.

Keywords

• directional data
• circular mean
• universal confidence sets
• non-asymptotic confidence sets
• mass concentration inequalities
• Hoeffding’s inequality