Related papers: A generalized Neyman-Pearson lemma for sublinear e…
We consider a problem of simple hypothesis testing using a randomized test via a tunable loss function proposed by Liao \textit{et al}. In this problem, we derive results that correspond to the Neyman--Pearson lemma, the Chernoff--Stein…
In this paper, under some weaker conditions, we give three laws of large numbers under sublinear expectations (capacities), which extend Peng's law of large numbers under sublinear expectations in [8] and Chen's strong law of large numbers…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a…
When faced with a small sample from a large universe of possible outcomes, scientists often turn to the venerable Good--Turing estimator. Despite its pedigree, however, this estimator comes with considerable drawbacks, such as the need to…
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…
The main purpose of this paper is to provide an asymptotically optimal test. The proposed statistic is of Neyman-Pearson-type when the parameters are estimated with a particular kind of estimators. It is shown that the proposed estimators…
We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
Particle physics experiments rely on the (generalised) likelihood ratio test (LRT) for searches and measurements, which consist of composite hypothesis tests. However, this test is not guaranteed to be optimal, as the Neyman-Pearson lemma…
We consider a family of conditional nonlinear expectations defined on the space of bounded random variables and indexed by the class of all the sub-sigma-algebras of a given underlying sigma-algebra. We show that if this family satisfies a…
We analyze hypotheses tests using classical results on large deviations to compare two models, each one described by a different H\"older Gibbs probability measure. One main difference to the classical hypothesis tests in Decision Theory is…
The Neyman-Pearson strategy for hypothesis testing can be employed for goodness of fit if the alternative hypothesis is selected from data by exploring a rich parametrised family of models, while controlling the impact of statistical…
The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…
In several interesting applications one is faced with the problem of simultaneous binary hypothesis testing and parameter estimation. Although such joint problems are not infrequent, there exist no systematic analysis in the literature that…
In fields that are mainly nonexperimental, such as economics and finance, it is inescapable to compute test statistics and confidence regions that are not probabilistically independent from previously examined data. The Bayesian and…
We address the following question in this paper: "What are the most robust statistical methods for social choice?'' By leveraging the theory of uniformly least favorable distributions in the Neyman-Pearson framework to finite models and…
We study the training dynamics of neural classifiers through the lens of binary hypothesis testing. We re-formalize classification as a collection of binary tests between class-conditional distributions induced by learned representations…
We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…
We consider a sequence of i.i.d. random variables $\{\xi_k\}$under a sublinear expectation $\mathbb{E}=\sup_{P\in\Theta}E_P$. We first give a new proof to the fact that, under each $P\in\Theta$, any cluster point of the empirical averages…