Andrés Aradillas Fernández, José Blanchet, José Luis Montiel Olea, Chen Qiu, Jörg Stoye, Lezhi Tan
arXiv 21 Nov 2025 · Econometrics
arXiv:2511.16925 · PDF · DOI · OpenAlex · Extracted main text
We consider a class of hypothesis testing problems where the null hypothesis postulates $M$ distributions for the observed data, and there is only one possible distribution under the alternative. We show that one can use a stochastic mirror descent routine for convex optimization to provably obtain - after finitely many iterations - both an approximate least-favorable distribution and a nearly optimal test, in a sense we make precise. Our theoretical results yield concrete recommendations about the algorithm's implementation, including its initial condition, its step size, and the number of iterations. Importantly, our suggested algorithm can be viewed as a slight variation of the algorithm suggested by Elliott, Müller, and Watson (2015), whose theoretical performance guarantees are unknown.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Elliott, G., U. K. Müller, and M. W. Watson (2015) Nearly optimal tests when a nuisance parameter is present under the null hypothesis | 1.000 | 16 | 6 | 100% |
| 2 | Bubeck, S (2015) Convex optimization: Algorithms and complexity | 0.956 | 8 | 4 | 88% |
| 3 | Krafft, O. and H. Witting (1967) Optimale tests und ungünstigste verteilungen | 0.811 | 4 | 2 | 100% |
| 4 | Moreira, H. and M. J. Moreira (2013) Contributions to the theory of optimal tests | 0.811 | 4 | 2 | 100% |
| 5 | Nemirovski, A., A. Juditsky, G. Lan, and A. Shapiro (2009) Robust stochastic approximation approach to stochastic programming | 0.737 | 3 | 3 | 67% |
| 6 | Dudley, R (2002) Real Analysis and Probability | 0.644 | 2 | 2 | 100% |
| 7 | Aradillas Fernández, A., J. Blanchet, J. L. Montiel Olea, C. Qiu, J.… (2025) Epsilon-Minimax Solutions of Statistical Decision Problems via the Hedge Algorithm | 0.644 | 2 | 2 | 100% |
| 8 | Nemirovski, A. and D. Yudin (1983) Problem Complexity and Method Efficiency in Optimization | 0.644 | 2 | 2 | 100% |
| 9 | Polyak, B. T. and A. B. Juditsky (1992) Acceleration of stochastic approximation by averaging | 0.644 | 2 | 2 | 100% |
| 10 | Ruppert, D (1988) Efficient estimations from a slowly convergent Robbins-Monro process, Tech | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 44 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Numerical Analysis of Test Optimality | 1.000 | 6 | 4 |