Multivariate Confidence Intervals
This addresses a gap in statistical visualization and analysis for multivariate data, offering a practical tool for researchers and analysts, though it is incremental as it builds on existing one-dimensional concepts.
The paper tackles the problem of extending confidence intervals to multivariate data, defining them so that data vectors can be outside a few intervals and still be within the confidence area, and shows that the resulting areas are informative and easy to interpret, with efficient approximate algorithms provided for this hard problem.
Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying confidence intervals to multivariate data. In this paper we define confidence intervals for multivariate data that extend the one-dimensional definition in a natural way. In our definition every variable is associated with its own confidence interval as usual, but a data vector can be outside of a few of these, and still be considered to be within the confidence area. We analyze the problem and show that the resulting confidence areas retain the good qualities of their one-dimensional counterparts: they are informative and easy to interpret. Furthermore, we show that the problem of finding multivariate confidence intervals is hard, but provide efficient approximate algorithms to solve the problem.