相关论文: Statistical Convergence and Convergence in Statist…

An equivalent condition for the product of elements of an independent random sample on a compact algebraic group converging in distribution to some random variable as the sample size increases is obtained. Namely, a limit distribution…

We introduce the notion of consistent error bound functions which provides a unifying framework for error bounds for multiple convex sets. This framework goes beyond the classical Lipschitzian and H\"olderian error bounds and includes…

Statistical inference is the science of drawing conclusions about some system from data. In modern signal processing and machine learning, inference is done in very high dimension: very many unknown characteristics about the system have to…

Clustering is part of unsupervised analysis methods that consist in grouping samples into homogeneous and separate subgroups of observations also called clusters. To interpret the clusters, statistical hypothesis testing is often used to…

Clustering is an underspecified task: there are no universal criteria for what makes a good clustering. This is especially true for relational data, where similarity can be based on the features of individuals, the relationships between…

We introduce statistical constraints, a declarative modelling tool that links statistics and constraint programming. We discuss two statistical constraints and some associated filtering algorithms. Finally, we illustrate applications to…

The problem of time-series clustering is considered in the case where each data-point is a sample generated by a piecewise stationary ergodic process. Stationary processes are perhaps the most general class of processes considered in…

Categorical data are common in educational and social science research; however, methods for its analysis are generally not covered in introductory statistics courses. This chapter overviews fundamental concepts and methods in categorical…

Time series clustering is essential in scientific applications, yet methods for functional time series, collections of infinite-dimensional curves treated as random elements in a Hilbert space, remain underdeveloped. This work presents…

We study the stochastic convergence of the Ces\`{a}ro mean of a sequence of random variables. These arise naturally in statistical problems that have a sequential component, where the sequence of random variables is typically derived from a…

The Central Limit Theorem provides a foundation for inferential statistics and hypothesis testing. It describes how standardized statistics behave under repeated sampling from large populations. However, if the size of the sample (n)…

In order to bring contraction analysis into the very fruitful and topical fields of stochastic and Bayesian systems, we extend here the theory describes in \cite{Lohmiller98} to random differential equations. We propose new definitions of…

Detecting and measuring confounding effects from data is a key challenge in causal inference. Existing methods frequently assume causal sufficiency, disregarding the presence of unobserved confounding variables. Causal sufficiency is both…

In this paper, we propose standard statistical tools as a solution to commonly highlighted problems in the explainability literature. Indeed, leveraging statistical estimators allows for a proper definition of explanations, enabling…

In quantum optics, measurement statistics -- for example, photocounting statistics -- are considered nonclassical if they cannot be reproduced with statistical mixtures of classical radiation fields. We have formulated a necessary and…

Measurement involves the determination of quantitative estimates of physical quantities from experiment, along with estimates of their associated uncertainties. Herewith an experimental system model is the key to extracting information from…

The leading term in the normal approximation to the distribution of Student's t statistic is derived in a general setting, with the sole assumption being that the sampled distribution is in the domain of attraction of a normal law. The form…

Stationarity is a very general, qualitative assumption, that can be assessed on the basis of application specifics. It is thus a rather attractive assumption to base statistical analysis on, especially for problems for which less general…

We introduce a new discrepancy score between two distributions that gives an indication on their similarity. While much research has been done to determine if two samples come from exactly the same distribution, much less research…

Logistic regression is an important statistical tool for assessing the probability of an outcome based upon some predictive variables. Standard methods can only deal with precisely known data, however many datasets have uncertainties which…