Asymptotic and finite-sample distributions of one- and two-sample empirical relative entropy

Battle Count: 69

The paper has moderate relevance to quantitative trading. The authors (particularly Garcin) have prior work on market efficiency testing using information-theoretic measures and time series analysis. The empirical relative entropy and its distributional properties can be used for change-point detection in financial time series, testing serial dependence, and building divergence tests between return distributions. However, the paper is primarily theoretical statistics rather than directly applicable to trading strategies. The finite-sample bounds could improve calibration of statistical tests used in financial econometrics.

The theoretical derivations are mathematically demanding (second-order Taylor expansions, Cardano's formula for cubic equations, multivariate Berry-Esseen theorem). However, the final results are relatively straightforward to implement: the asymptotic chi-squared approximation is trivial, Agrawal's concentration bounds (M3) have simple closed-form expressions, and the Berry-Esseen bounds require computing explicit constants and solving cubic equations. The two-sample case adds complexity through the reverse Pinsker decomposition and Laplace regularization.

The paper provides complete mathematical proofs in appendices (A-D) and describes simulation parameters (n=100, k=4, 10,000 simulations, uniform distribution). However, no code repository or software implementation is provided. The theoretical results are fully specified with explicit constants, making them reproducible analytically. The simulation study is described sufficiently to replicate but no code is shared.