New paper derives distributions for empirical relative entropy, offering finite-sample results that improve how quants test whether two return distributions differ.
A new paper on arXiv examines the asymptotic and finite-sample distributions of one- and two-sample empirical relative entropy. The work, by an author not named in the summary, addresses the statistical behavior of the Kullback–Leibler divergence estimate when the underlying distributions are unknown and must be estimated from data.
For quantitative market analysis, the paper's results could improve how researchers test whether two return distributions differ – a common problem in factor analysis, regime detection, and backtesting. The finite-sample distributional results are especially relevant for smaller datasets, where asymptotic approximations often fail.
Apple (AAPL) is a heavily traded stock whose return distribution shifts with product cycles and regulatory news. The methods described in the paper could be used to test, for example, whether the distribution of AAPL returns before and after an earnings call are statistically distinguishable, using a sample size that matches the actual number of trading days in each period.
The paper is available on arXiv under the identifier 2512.16411.
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