On inference of boxplot symbolic data: applications in climatology

Abstract. This paper presents a pioneering study on the inference of boxplot-valued data using both Bayesian and frequentist approaches within a multivariate framework. This approach leverages complex yet intuitive representations to make large datasets more manageable and enhance their interpretability, which is invaluable in the age of big data. Boxplot-valued data are particularly important due to their ability to capture the inherent variability and distributional characteristics of complex datasets. In our study, we propose novel methodologies for parameter estimation and density estimation for boxplot-valued data and apply these techniques to climatological data. Specifically, we utilize data from the Berkeley Earth Surface Temperature Study, which aggregates 1.6 billion temperature reports from 16 pre-existing archives affiliated with the Lawrence Berkeley National Laboratory. Our methods are validated through extensive simulations comparing the efficiency and accuracy of Bayesian and frequentist estimators. We demonstrate the practical applicability of our approach by analyzing summer average temperatures across various European countries. The proposed techniques provide robust tools for analyzing complex data structures, offering valuable insights into climatic trends and variations. Our study highlights the advantages and limitations of each inferential method, offering guidance for future research and applications in the field of climatology.