Estimation of discrete distributions with high probability under $\chi^2$-divergence

A recent study delves into the high-probability estimation of discrete distributions using chi-squared divergence loss, revealing significant insights. While the minimax risk in expectation is well understood, this research sheds light on its high-probability counterpart, which has been less explored. The authors present precise upper and lower bounds for the classical Laplace estimator, demonstrating its optimal performance without depending on confidence levels. This advancement is crucial for statisticians and data scientists, as it enhances the understanding of estimation techniques in statistical analysis.