Related papers: On statistical independence and density independen…
In this paper we provide a theoretical analysis of counterfactual invariance. We present a variety of existing definitions, study how they relate to each other and what their graphical implications are. We then turn to the current major…
We consider the problem of independence testing for two univariate random variables in a sequential setting. By leveraging recent developments on safe, anytime-valid inference, we propose a test with time-uniform type I error control and…
The sensitivity properties of intermittent control are analysed and the conditions for a limit cycle derived theoretically and verified by simulation.
Frequentist-style large-sample properties of Bayesian posterior distributions, such as consistency and convergence rates, are important considerations in nonparametric problems. In this paper we give an analysis of Bayesian asymptotics…
The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial…
A general link between geometry and intermittency in passive scalar turbulence is established. Intermittency is qualitatively traced back to events where tracer particles stay for anomalousy long times in degenerate geometries characterized…
The survey is devoted to the combinatorial and metric theory of filtrations, i.\,e., decreasing sequences of $\sigma$-algebras in measure spaces or decreasing sequences of subalgebras of certain algebras. One of the key notions, that of…
The reconstruction of the parameter of the model by the measurement of the random variable depending on this parameter is one of the main tasks of statistics. In the paper the notion of the statistically dual distributions is introduced.…
We study the problems of sequential nonparametric two-sample and independence testing. Sequential tests process data online and allow using observed data to decide whether to stop and reject the null hypothesis or to collect more data,…
This work is devoted to the definition and the analysis of the effective viscosity associated with a random suspension of small rigid particles in a steady Stokes fluid. While previous works on the topic have been conveniently assuming that…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is esablished. A set of combinations of expectation values whose value does not in general depend…
This paper develops an intuitive concept of perfect dependence between two variables of which at least one has a nominal scale. Perfect dependence is attainable for all marginal distributions. It furthermore proposes a set of dependence…
We consider the nonparametric estimation of the density function of weakly and strongly dependent processes with noisy observations. We show that in the ordinary smooth case the optimal bandwidth choice can be influenced by long range…
In this article we define a metric on C(S1; S1). Also, we give some density results in C(S^1; S^1).
We consider an approach for testing the hypothesis that two realizations of the random variables in the form of histograms are taken from the same statistical population (i.e. two histograms are drawn from the same distribution). The…
We construct a function on the real line supported on a set of finite measure whose spectrum has density zero.
A fundamental task in statistical learning is quantifying the joint dependence or association between two continuous random variables. We introduce a novel, fully non-parametric measure that assesses the degree of association between…
We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information in relational databases. The concepts of possible and certain independence are proposed, and…
Statistical physics is used to investigate independent component analysis with polynomial contrast functions. While the replica method fails, an adapted cavity approach yields valid results. The learning curves, obtained in a suitable…
This article discusses dependence on initial conditions in natural and social sciences with focus on physical science. The main focus is on the newly discovered rough dependence on initial data.