On Entropy Based Diversity Measures: Statistical Efficiency and Robustness Considerations

ABSTRACT

We consider the problem of estimating diversity measures for a stratified population and discuss a general formulation for the entropy based diversity measures which includes the previously used entropies as well as a newly proposed family of logarithmic norm entropy (LNE) measures. Our main focus in this work is the consideration of statistical properties (asymptotic efficiency and finite sample robustness) of the sample estimates of such entropy-based diversity measures for their validation and appropriate recommendations. Our proposed LNE based diversity is indeed seen to provide the best trade-offs at an appropriately chosen tuning parameter. Along the way, we also show that the second best candidates are the hypoentropy based diversities justifying their consideration by Leandro Pardo and his colleagues in 1993 over the other entropy families existing at that time. We finally apply the proposed LNE based measure to examine the demographic (age and gender based) diversities among Covid-19 deaths in USA. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.