Related papers: Variational formulas for the power of the binary h…
The classical binary hypothesis testing problem is revisited. We notice that when one of the hypotheses is composite, there is an inherent difficulty in defining an optimality criterion that is both informative and well-justified. For…
Statistical dependence between hypotheses poses a significant challenge to the stability of large scale multiple hypotheses testing. Ignoring it often results in an unacceptably large spread in the false positive proportion even though the…
Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…
Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the…
We investigate the discrimination of two candidates of an unknown parameter in quantum systems with continuous weak measurement, inspired by the application of hypothesis testing in distinguish-ing two Hamiltonians [Kiilerich and M{\o}lmer,…
We give a new, self-contained proof of the multidimensional central limit theorem using the technique of ``doubling variables," which is traditionally used to prove uniqueness of solutions of partial differential equations (PDEs). Our…
We introduce fully nonparametric two-sample tests for testing the null hypothesis that the samples come from the same distribution if the values are only indirectly given via current status censoring. The tests are based on the likelihood…
We use a system of first-order partial differential equations that characterize the moment generating function of the $d$-variate standard normal distribution to construct a class of affine invariant tests for normality in any dimension. We…
We propose three novel consistent specification tests for quantile regression models which generalize former tests in three ways. First, we allow the covariate effects to be quantile-dependent and nonlinear. Second, we allow parameterizing…
We study the problem of mismatched binary hypothesis testing between i.i.d. distributions. We analyze the tradeoff between the pairwise error probability exponents when the actual distributions generating the observation are different from…
This work investigates binary hypothesis testing between $H_0\sim P_0$ and $H_1\sim P_1$ in the finite-sample regime under asymmetric error constraints. By employing the ``reverse" R\'enyi divergence, we derive novel non-asymptotic bounds…
This article introduces probabilistic disjunctive normal forms (PDNFs) as a framework for representing and reasoning about uncertainty in logical systems. Unlike classical DNFs, PDNFs assign real-valued weights to variables, encoding…
Using cumulative residual processes, we propose joint goodness-of-fit tests for conditional means and variances functions in the context of nonlinear time series with martingale difference innovations. The main challenge comes from the fact…
Fine-tuning large language models (LLMs) on reasoning benchmarks via reinforcement learning requires a specific reward function, often binary, for each benchmark. This comes with two potential limitations: the need to design the reward, and…
We interpret likelihood-based test functions from a geometric perspective where the Kullback-Leibler (KL) divergence is adopted to quantify the distance from a distribution to another. Such a test function can be seen as a sub-Gaussian…
We introduce estimation and test procedures through divergence optimization for discrete or continuous parametric models. This approach is based on a new dual representation for divergences. We treat point estimation and tests for simple…
Data-driven most powerful tests are statistical hypothesis decision-making tools that deliver the greatest power against a fixed null hypothesis among all corresponding data-based tests of a given size. When the underlying data…
While calibration of probabilistic predictions has been widely studied, this paper rather addresses calibration of likelihood functions. This has been discussed, especially in biometrics, in cases with only two exhaustive and mutually…
Bayesian sample size calculations in clinical trials usually rely on complex Monte Carlo simulations in practice. Obtaining bounds on Bayesian notions of the false-positive rate and power often lack closed-form or approximate numerical…
How should we evaluate the effect of a policy on the likelihood of an undesirable event, such as conflict? The significance test has three limitations. First, relying on statistical significance misses the fact that uncertainty is a…