arXiv subjects

Gökhan Gül

Publications and source records attributed to Gökhan Gül.

8 recordsLinked to original sources

arXiv2026

A Structural Separation Between Chernoff and Convex-Order Optimality in Robust Testing

In classical robust hypothesis testing, least favorable distributions often simultaneously maximize all Chernoff $u$-affinities and minimize all $f$-divergences. This paper identifies the structural mechanism that causes this equivalence to fail in general: the cone generated by fractional power functions $\{x^u\}_{u\in(0,1)}$ is strictly smaller than the cone of convex functions, inducing a separation between fractional-moment dominance and convex-order dominance. An explicit minimal counterexample is constructed on a three-point probability space, with convex, compact uncertainty classes and uniformly bounded likelihood ratios, for which a single pair maximizes all Chernoff functionals uniformly yet fails to minimize a convex $f$-divergence. It is further proved that no such separation can occur on a two-point space. Sufficient conditions for equivalence -- including stochastic ordering of likelihood ratios -- are discussed, and an open characterization problem in the geometry of moment cones is highlighted.

math.ST↗

arXiv2026

Asymptotically Minimax Robust Hypothesis Testing

The design of asymptotically minimax robust hypothesis testing is formalized for the Bayesian and Neyman-Pearson tests of Type-I and Type-II. The uncertainty classes based on the KL-divergence, $α$-divergence, symmetrized $α$-divergence, total variation distance, as well as the band model, moment classes and p-point classes are considered. Implications between single-sample-, all-sample- and asymptotic minimax robustness are derived. Existence and uniqueness of asymptotically minimax robust tests are proven using Sion's minimax theorem and the Karush-Kuhn-Tucker multipliers. The least favorable distributions and the corresponding robust likelihood ratio functions are derived in parametric forms, which can then be determined by solving a system of equations. The proposed theory proves that Dabak's design does not produce any asymptotically minimax robust test. Furthermore, it also generalizes the earlier works by Huber and Kassam by allowing analytical derivations, hence, providing answers to the questions 'how?', which were left unanswered. Simulations are provided to exemplify and evaluate the theoretical derivations.

cs.IT↗

arXiv2026

From Asymptotic to Finite-Sample Minimax Robust Hypothesis Testing

This paper establishes a formal connection between finite-sample and asymptotically minimax robust hypothesis testing under distributional uncertainty. It is shown that, whenever a finite-sample minimax robust test exists, it coincides with the solution of the corresponding asymptotic minimax problem. This result enables the analytical derivation of finite-sample minimax robust tests using asymptotic theory, bypassing the need for heuristic constructions. The total variation distance and band model are examined as representative uncertainty classes. For each, the least favorable distributions and corresponding robust likelihood ratio functions are derived in parametric form. In the total variation case, the new derivation generalizes earlier results by allowing unequal robustness parameters. The theory also explains and systematizes previously heuristic designs. Simulations are provided to illustrate the theoretical results.

math.ST↗

arXiv2026

Asymptotically Minimax Robust Likelihood Ratio Test

This paper develops a unified framework for asymptotically minimax robust hypothesis testing under distributional uncertainty, applicable to both Bayesian and Neyman--Pearson formulations (Type-I and Type-II). Uncertainty classes based on the KL-divergence, $α$-divergence, and its symmetrized variant are considered. Using Sion's minimax theorem and Karush-Kuhn-Tucker conditions, the existence and uniqueness of the resulting robust tests are established. The least favorable distributions and corresponding robust likelihood ratio functions are derived in closed parametric forms, enabling computation via systems of nonlinear equations. It is proven that Dabak's approach does not yield an asymptotically minimax robust test. The proposed theory generalizes earlier work by offering a more systematic and comprehensive derivation of robust tests. Numerical simulations confirm the theoretical results and illustrate the behavior of the derived robust tests.

math.ST↗

arXiv2017

Minimax Robust Decentralized Detection in Parallel Sensor Networks

Minimax robust decentralized detection is studied for parallel sensor networks. Random variables corresponding to sensor observations are assumed to follow a distribution function, which belongs to an uncertainty class. It has been proven that, for some uncertainty classes, if all probability distributions are absolutely continuous with respect to a common measure, the joint stochastic boundedness property, which is the fundamental rule for the derivations in Veerevalli's work, does not hold. This raises a natural question whether minimax robust decentralized detection is possible if the uncertainty classes do not own this property. The answer to this question has been shown to be positive, which leads to a generalization of the work of Veerevalli. Moreover, due to a direct consequence of Tsitsiklis's work, quantization functions at the sensors are not required to be monotone. For the proposed model, some specific examples have been provided and possible generalizations have been discussed.

cs.IT↗

arXiv2016

Theoretical Bounds in Minimax Decentralized Hypothesis Testing

Minimax decentralized detection is studied under two scenarios: with and without a fusion center when the source of uncertainty is the Bayesian prior. When there is no fusion center, the constraints in the network design are determined. Both for a single decision maker and multiple decision makers, the maximum loss in detection performance due to minimax decision making is obtained. In the presence of a fusion center, the maximum loss of detection performance between with- and without fusion center networks is derived assuming that both networks are minimax robust. The results are finally generalized.

cs.IT↗

arXiv2016

Robust Hypothesis Testing with $α$-Divergence

A robust minimax test for two composite hypotheses, which are determined by the neighborhoods of two nominal distributions with respect to a set of distances - called $α-$divergence distances, is proposed. Sion's minimax theorem is adopted to characterize the saddle value condition. Least favorable distributions, the robust decision rule and the robust likelihood ratio test are derived. If the nominal probability distributions satisfy a symmetry condition, the design procedure is shown to be simplified considerably. The parameters controlling the degree of robustness are bounded from above and the bounds are shown to be resulting from a solution of a set of equations. The simulations performed evaluate and exemplify the theoretical derivations.

stat.OT↗

arXiv2015

Minimax Robust Hypothesis Testing

The minimax robust hypothesis testing problem for the case where the nominal probability distributions are subject to both modeling errors and outliers is studied in twofold. First, a robust hypothesis testing scheme based on a relative entropy distance is designed. This approach provides robustness with respect to modeling errors and is a generalization of a previous work proposed by Levy. Then, it is shown that this scheme can be combined with Huber's robust test through a composite uncertainty class, for which the existence of a saddle value condition is also proven. The composite version of the robust hypothesis testing scheme as well as the individual robust tests are extended to fixed sample size and sequential probability ratio tests. The composite model is shown to extend to robust estimation problems as well. Simulation results are provided to validate the proposed assertions.

cs.IT↗