相关论文: Lower k-record values from unit-Gompertz distribut…
We derive an expression for the nearest-neighbor spacing distribution $P(s)$ of the energy levels of quantum systems with intermediate dynamics between regularity and chaos and missing levels due to random experimental errors. The…
In Selk and Gertheiss (2022) a nonparametric prediction method for models with multiple functional and categorical covariates is introduced. The dependent variable can be categorical (binary or multi-class) or continuous, thus both…
Large language models (LLMs) are often confidently wrong, making reliable uncertainty estimation (UE) essential. Output-based heuristics are cheap but brittle, while probing internal representations is effective yet high-dimensional and…
We study the distribution of hard-, soft-, and adaptive soft-thresholding estimators within a linear regression model where the number of parameters k can depend on sample size n and may diverge with n. In addition to the case of known…
Copulas have gained widespread popularity as statistical models to represent dependence structures between multiple variables in various applications. The minimum information copula, given a finite number of constraints in advance, emerges…
The truncated Korteweg-De Vries (TKdV) system, a shallow-water wave model with Hamiltonian structure that exhibits weakly turbulent dynamics, has been found to accurately predict the anomalous wave statistics observed in recent laboratory…
A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…
Gamma-Ray Bursts (GRBs) are known to be unpredictable in time and position. A few (observationally) exceptional events have been observed, as GRB221009A that stands out for its fluence and peak flux, being orders of magnitude higher than…
This manuscript develops a general purpose inner-product norm for the Kendall \(\tau\) and Spearman's \(\rho\), which operates as an unbiased MLE even in the presence of ties. We derive and prove the strict sub-Gaussianity of the Kemeny…
In this paper, decision theory was used to derive Bayes and minimax decision rules to estimate allelic frequencies and to explore their admissibility. Decision rules with uniformly smallest risk usually do not exist and one approach to…
In this study, simultaneous predictive distributions for independent Poisson observables were considered and the performance of predictive distributions was evaluated using the Kullback-Leibler (K-L) loss. This study proposes a class of…
Predicting the outcomes of quantum measurements is a cornerstone of quantum information theory and a key resource for quantum technologies. Here, we introduce a comprehensive framework for quantifying the predictability of measurements on a…
The generalized Kullback-Leibler divergence (K-Ld) in Tsallis statistics [constrained by the additive duality of generalized statistics (dual generalized K-Ld)] is here reconciled with the theory of Bregman divergences for expectations…
A popular approach for testing if two univariate random variables are statistically independent consists of partitioning the sample space into bins, and evaluating a test statistic on the binned data. The partition size matters, and the…
This study aims to predict failure times for some units in some lifetime experiments. In some practical situations, the experimenter may not be able to register the failure times of all units during the experiment. Recently, this situation…
We study the problem of sampling an approximately uniformly random satisfying assignment for atomic constraint satisfaction problems i.e. where each constraint is violated by only one assignment to its variables. Let $p$ denote the maximum…
The distribution of the spacing, or the difference between consecutive order statistics, is known only for uniform and exponential random variates. We add here logistic and Gumbel variates, and present an estimator for distributions with a…
The local spectral statistics of random matrices forms distinct universality classes, strongly depending on the position in the spectrum. Surprisingly, the spacing between consecutive eigenvalues at the spectral edges has received little…
We obtain optimal Gaussian concentration bounds (GCBs) for stochastic chains of unbounded memory (SCUMs) on countable alphabets. These stochastic processes are also known as "chains with complete connections" or "$g$-measures". We consider…
Over the past decade, the low-degree heuristic has been used to estimate the algorithmic thresholds for a wide range of average-case planted vs null distinguishing problems. Such results rely on the hypothesis that if the low-degree moments…