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1. Likelihood-Free Hypothesis Testing

   https://doi.org/10.1109/TIT.2024.3412107  

   Gerber, Patrik; Polyanskiy, Yury (November 2024, IEEE Transactions on Information Theory)
2. Maximum Likelihood Estimation of Optimal Receiver Operating Characteristic Curves From Likelihood Ratio Observations

   https://doi.org/10.1109/ISIT50566.2022.9834765  

   Hajek, Bruce; Kang, Xiaohan (June 2022, IEEE International Symposium on Information Theory)

   The optimal receiver operating characteristic (ROC) curve, giving the maximum probability of detection as a function of the probability of false alarm, is a key information-theoretic indicator of the difficulty of a binary hypothesis testing problem (BHT). It is well known that the optimal ROC curve for a given BHT, corresponding to the likelihood ratio test, is theoretically determined by the probability distribution of the observed data under each of the two hypotheses. In some cases, these two distributions may be unknown or computationally intractable, but independent samples of the likelihood ratio can be observed. This raises the problem of estimating the optimal ROC for a BHT from such samples. The maximum likelihood estimator of the optimal ROC curve is derived, and it is shown to converge to the true optimal ROC curve in the \levy\ metric, as the number of observations tends to infinity. A classical empirical estimator, based on estimating the two types of error probabilities from two separate sets of samples, is also considered. The maximum likelihood estimator is observed in simulation experiments to be considerably more accurate than the empirical estimator, especially when the number of samples obtained under one of the two hypotheses is small. The area under the maximum likelihood estimator is derived; it is a consistent estimator of the true area under the optimal ROC curve. 

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3. Maximum Likelihood Estimation of Optimal Receiver Operating Characteristic Curves From Likelihood Ratio Observations

   https://doi.org/10.1109/TIT.2025.3595488  

   Hajek, Bruce; Kang, Xiaohan (October 2025, IEEE Transactions on Information Theory)
4. High-dimensional empirical likelihood inference

   https://doi.org/10.1093/biomet/asaa051  

   Chang, Jinyuan; Chen, Song Xi; Tang, Cheng Yong; Wu, Tong Tong (October 2020, Biometrika)

   null (Ed.)

   Summary High-dimensional statistical inference with general estimating equations is challenging and remains little explored. We study two problems in the area: confidence set estimation for multiple components of the model parameters, and model specifications tests. First, we propose to construct a new set of estimating equations such that the impact from estimating the high-dimensional nuisance parameters becomes asymptotically negligible. The new construction enables us to estimate a valid confidence region by empirical likelihood ratio. Second, we propose a test statistic as the maximum of the marginal empirical likelihood ratios to quantify data evidence against the model specification. Our theory establishes the validity of the proposed empirical likelihood approaches, accommodating over-identification and exponentially growing data dimensionality. Numerical studies demonstrate promising performance and potential practical benefits of the new methods. 

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5. Unbiased Metamodeling via Likelihood Ratios

   Dong, J. Feng (December 2018, Proceedings of the 2018 Winter Simulation Conference)

   Metamodeling has been a topic of longstanding interest in stochastic simulation because of the usefulness of metamodels for optimization, sensitivity, and real- or near-real-time decision making. Experiment design is the foundation of classical metamodeling: an effective experiment design uncovers the spatial relationships among the design/decision variables and the simulation response; therefore, more design points, providing better coverage of space, is almost always better. However, metamodeling based on likelihood ratios (LRs) turns the design question on its head: each design point provides an unbiased prediction of the response at any other location in space, but perhaps with such inflated variance as to be counterproductive. Thus, the question becomes more which design points to employ for prediction and less where to place them. In this paper we take the first comprehensive look at LR metamodeling, categorizing both the various types of LR metamodels and the contexts in which they might be employed. 

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