Search

The User-Managed Access (UMA) extension to OAuth 2.0 is a promising candidate for increasing Digital Trust in personal data ecosystems like Solid. With minor modifications, it can achieve many requirements regarding usage control and transaction contextualization, even though additional specification is needed to address delegation of control and retraction of usage policies.

In this paper, we consider partial sums of martingale differences weighted by random variables drawn uniformly on the sphere, and globally independent of the martingale differences. Combining Lindeberg's method and a series of arguments due to Bobkov, Chistyakov and G{\"o}tze, we show that the Kolmogorov distance between the distribution of these weighted sums and the limiting Gaussian is "super-fast" of order (log n)^2 /n, under conditions allowing us to control the higher-order conditional moments of the martingale differences. We give an application of this result to the least squares estimator of the slope in the linear model with Gaussian design.

Following White's approach of robust multiple linear regression, we give asymptotic confidence intervals for the multiple correlation coefficient R2 under minimal moment conditions. We also give the asymptotic joint distribution of the empirical estimators of the individual R2's. Through different sets of simulations, we show that the procedure is indeed robust (contrary to the procedure involving the near exact distribution of the empirical estimator of R2 is the multivariate Gaussian case) and can be also applied to count linear regression.

Transport in complex networks can describe a variety of natural and human-engineered processes including biological, societal and technological ones. However, how the properties of the source and drain nodes can affect transport subject to random failures, attacks or maintenance optimization in the network remain unknown. In this paper, the effects of both the distance between the source and drain nodes and of the degree of the source node on the time of transport collapse are studied in scale-free and lattice-based transport networks. These effects are numerically evaluated for two strategies, which employ either transport-based or random link removal. Scale-free networks with small distances are found to result in larger times of collapse. In lattice-based networks, both the dimension and boundary conditions are shown to have a major effect on the time of collapse. We also show that adding a direct link between the source and the drain increases the robustness of scale-free networks when subject to random link removals. Interestingly, the distribution of the times of collapse is then similar to the one of lattice-based networks.

We prove the Almost Sure Invariance Principle (ASIP) with close to optimal error rates for nonuniformly hyperbolic maps. We do not assume exponential contraction along stable leaves, therefore our result covers in particular slowly mixing invertible dynamical systems as Bunimovich flowers, billiards with flat points as in Chernov and Zhang (2005) and Wojtkowski' (1990) system of two falling balls. For these examples, the ASIP is a new result, not covered by prior works for various reasons, notably because in absence of exponential contraction along stable leaves, it is challenging to employ the so-called Sinai's trick (Sinai 1972, Bowen 1975) of reducing a nonuniformly hyperbolic system to a nonuniformly expanding one. Our strategy follows our previous papers on the ASIP for nonuniformly expanding maps, where we build a semiconjugacy to a specific renewal Markov shift and adapt the argument of Berkes, Liu and Wu (2014). The main difference is that now the Markov shift is two-sided, the observables depend on the full trajectory, both the future and the past.

In this paper, we give precise rates of convergence in the strong invariance principle for stationary sequences of bounded real-valued random variables satisfying weak dependence conditions. One of the main ingredients is a new Fuk-Nagaev type inequality for a class of weakly dependent sequences. We describe also several classes of processes to which our results apply.

We give rates of convergence in the almost sure invariance principle for sums of dependent random variables with semi exponential tails, whose coupling coefficients decrease at a subexponential rate. We show that the rates in the strong invariance principle are in powers of log n. We apply our results to iid products of random matrices.

A new multivariate density estimator for stationary sequences is obtained by Fourier inversion of the thresholded empirical characteristic function. This estimator does not depend on the choice of parameters related to the smoothness of the density; it is directly adaptive. We establish oracle inequalities valid for independent, $\alpha$-mixing and $\tau$-mixing sequences, which allows us to derive optimal convergence rates, up to a logarithmic loss. On general anisotropic Sobolev classes, the estimator adapts to the regularity of the unknown density but also achieves directional adaptivity. In particular, if A is an invertible matrix, if the observations are drawn from X $\in$ R^d , d $\ge$ 1, it achieves the rate implied by the regularity of AX, which may be more regular than X. The estimator is easy to implement and numerically efficient. It depends on the calibration of a parameter for which we propose an innovative numerical selection procedure, using the Euler characteristic of the thresholded areas.

The R package robusTest offers corrected versions of several common tests in bivariate statistics. We point out the limitations of these tests in their classical versions, some of which are well known such as robustness or calibration problems, and provide simple alternatives that can be easily used instead. The classical tests and theirs robust alternatives are compared through a small simulation study. The latter emphasizes the superiority of robust versions of the test of interest. Finally, an illustration of correlation's tests on a real data set is also provided.

In this paper, we consider a generalization of the elephant random walk model. Compared to the usual elephant random walk, an interesting feature of this model is that the step sizes form a sequence of positive independent and identically distributed random variables instead of a fixed constant. For this model, we establish the law of the iterated logarithm, the central limit theorem, and we obtain rates of convergence in the central limit theorem with respect to the Kologmorov, Zolotarev and Wasserstein distances. We emphasize that, even in case of the usual elephant random walk, our results concerning the rates of convergence in the central limit theorem are new.

We prove a strong invariance principle for the Kantorovich distance between the empiricaldistribution and the marginal distribution of stationary $\alpha$-mixing sequences.

We study stochastic properties of the norm cocycle associated with iid products of positive matrices. We obtain the almost sure invariance principle (ASIP) with rate o(n 1/p) under the optimal condition of a moment or order p > 2 and the Berry-Esseen theorem with rate O(1/ $\sqrt$ n) under the optimal condition of a moment of order 3. The results are also valid for the matrix norm. For the matrix coefficients, we also have the ASIP but we obtain only partial results for the Berry-Esseen theorem. The proofs make use of coupling coefficients that surprisingly decay exponentially fast to 0 while there is only a polynomial decay in the case of invertible matrices. All the results are actually valid in the context of iid products of matrices leaving invariant a suitable cone.

In this paper, we give estimates of the quadratic transportation cost in the conditional central limit theorem for a large class of dependent sequences. Applications to irreducible Markov chains, dynamical systems generated by intermittent maps and $\tau$-mixing sequences are given.

Let $A_n= \varepsilon_n \cdots \varepsilon_1$, where $(\varepsilon_n)_{n \geq 1}$ is a sequence of independent random matrices taking values in $ GL_d(\mathbb R)$, $d \geq 2$, with common distribution $\mu$. In this paper, under standard assumptions on $\mu$ (strong irreducibility and proximality), we prove Berry-Esseen type theorems for $\log ( \Vert A_n \Vert)$ when $\mu$ has a polynomial moment. More precisely, we get the rate $((\log n) / n)^{q/2-1}$ when $\mu$ has a moment of order $q \in ]2,3]$ and the rate $1/ \sqrt{n} $ when $\mu$ has a moment of order $4$, which significantly improves earlier results in this setting.

Linkages between research outputs are crucial in the scholarly knowledge graph. They include online citations, but also links between versions that differ according to various dimensions and links to resources that were used to arrive at research results. In current scholarly communication systems this information is only made available post factum and is obtained via elaborate batch processing. In this paper we report on work aimed at making linkages available in real-time, in which an alternative, decentralised scholarly communication network is considered that consists of interacting data nodes that host artifacts and service nodes that add value to artifacts. The first result of this work, the "Event Notifications in Value-Adding Networks" specification, details interoperability requirements for the exchange of real-time life-cycle information pertaining to artifacts using Linked Data Notifications. In an experiment, we applied our specification to one particular use-case: distributing Scholix data-literature links to a network of Belgian institutional repositories by a national service node. The results of our experiment confirm the potential of our approach and provide a framework to create a network of interacting nodes implementing the core scholarly functions (registration, certification, awareness and archiving) in a decentralized and decoupled way., Comment: 12 pages, 2 figures, Accepted at the 26th International Conference on Theory and Practice of Digital Libraries, Padua, Italy

We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples showing that the obtained upper bounds are essentially optimal.

We give rates of convergence in the Central Limit Theorem for the coefficients and the spectral radius of the left random walk on GLd(R), assuming the existence of an exponential or polynomial moment.

In this paper, we give rates of convergence, for minimal distances and for the uniform distance, between the law of partial sums of martingale differences and thelimiting Gaussian distribution. More precisely, denoting by $P_{X}$ the law of a random variable $X$ and by $G_{a}$ the normal distribution ${\mathcal N} (0,a)$, we are interested by giving quantitative estimates for the convergence of $P_{S_n/\sqrt{V_n}}$ to $G_1$, where $S_n$ is the partial sum associated with either martingale differences sequences or more general dependent sequences, and $V_n= {\rm Var}(S_n)$. Applications to linear statistics, non stationary $\rho$-mixing sequences and sequential dynamical systems are given.

In this paper, we study the nonparametric linear model, when the error process is a dependent Gaussian process. We focus on the estimation of the mean vector via a model selection approach. We first give the general theoretical form of the penalty function, ensuring that the penalized estimator among a collection of models satisfies an oracle inequality. Then we derive a penalty shape involving the spectral radius of the covariance matrix of the errors, which can be chosen proportional to the dimension when the error process is stationary and short range dependent. However, this penalty can be too rough in some cases, in particular when the error process is long range dependent. In a second part, we focus on the fixed-design regression model assuming that the error process is a stationary Gaussian process. We propose a model selection procedure in order to estimate the mean function via piecewise polynomials on a regular partition, when the error process is either short range dependent, long range dependent or anti-persistent. We present different kinds of penalties, depending on the memory of the process. For each case, an adaptive estimator is built, and the rates of convergence are computed. Thanks to several sets of simulations, we study the performance of these different penalties for all types of errors (short memory, long memory and anti-persistent errors). Finally, we give an application of our method to the well-known Nile data, which clearly shows that the type of dependence of the error process must be taken into account., Comment: 30 pages, 14 figures

In this paper, we give explicit rates in the central limit theorem and in the almost sure invariance principle for general R d-valued cocycles that appear in the study of the left random walk on linear groups. Our method of proof lies on a suitable martingale approximation and on a careful estimation of some coupling coefficients linked with the underlying Markov structure. Concerning the martingale part, the available results in the literature are not accurate enough to give almost optimal rates whether in the central limit theorem for the Wasserstein distance, or in the strong approximation. A part of this paper is devoted to circumvent this issue. We then exhibit near optimal rates both in the central limit theorem in terms of Wasserstein distance and in the almost sure invariance principle for R d-valued martingales with stationary increments having moments of order p $\in$]2, 3] (the case of sequences of reversed martingale differences is also considered). Note also that, as an application of our results for general R d-valued cocycles, a special attention is paid to the Iwasawa cocycle and the Cartan projection for reductive Lie groups.

We consider a class of non-homogeneous Markov chains, that contains many natural examples. Next, using martingale methods, we establish some deviation and moment inequalities for separately Lipschitz functions of such a chain, under moment conditions on some dominating random variables., Comment: 18 pages

This paper introduces the R package slm which stands for Stationary Linear Models. The package contains a set of statistical procedures for linear regression in the general context where the error process is strictly stationary with short memory. We work in the setting of Hannan (1973), who proved the asymptotic normality of the (normalized) least squares estimators (LSE) under very mild conditions on the error process. We propose different ways to estimate the asymptotic covariance matrix of the LSE, and then to correct the type I error rates of the usual tests on the parameters (as well as confidence intervals). The procedures are evaluated through different sets of simulations, and two examples of real datasets are studied., Comment: 31 pages, 11 figures, 5 tables. The associated R package 'slm' is available on the CRAN website (https://cran.r-project.org/index.html) or on the GitHub website (https://github.com/E-Caron/slm)

Let (X k) be a strictly stationary sequence of random variables with values in some Polish space E and common marginal $\mu$, and (A k) k>0 be a sequence of Borel sets in E. In this paper, we give some conditions on (X k) and (A k) under which the events {X k $\in$ A k } satisfy the Borel-Cantelli (or strong Borel-Cantelli) property. In particular we prove that, if $\mu$(lim sup n A n) > 0, the Borel-Cantelli property holds for any absolutely regular sequence. In case where the A k 's are nested, we show, on some examples, that a rate of convergence of the mixing coefficients is needed. Finally we give extensions of these results to weaker notions of dependence, yielding applications to non-irreducible Markov chains and dynamical systems.

For a large class of quickly mixing dynamical systems, we prove that the error in the almost sure approximation with a Brownian motion is of order O((log n)^a) with a $\ge$ 2. Specifically, we consider nonuniformly expanding maps with exponential and stretched exponential decay of correlations, with one-dimensional H{\"o}lder continuous observables.

We establish some deviation inequalities, moment bounds and almost sure results for the Wasserstein distance of order p $\in$ [1, $\infty$) between the empirical measure of independent and identically distributed R d-valued random variables and the common distribution of the variables. We only assume the existence of a (strong or weak) moment of order rp for some r > 1, and we discuss the optimality of the bounds. Mathematics subject classification. 60B10, 60F10, 60F15, 60E15.

We prove the one-dimensional almost sure invariance principle with essentially optimal rates for slowly (polynomially) mixing deterministic dynamical systems, such as Pomeau-Manneville intermittent maps, with H\"older continuous observables. Our rates have form $o(n^\gamma L(n))$, where $L(n)$ is a slowly varying function and $\gamma$ is determined by the speed of mixing. We strongly improve previous results where the best available rates did not exceed $O(n^{1/4})$. To break the $O(n^{1/4})$ barrier, we represent the dynamics as a Young-tower-like Markov chain and adapt the methods of Berkes-Liu-Wu and Cuny-Dedecker-Merlev\`ede on the Koml\'os-Major-Tusn\'ady approximation for dependent processes., Comment: 34 pages

In this paper we propose an alternative to the coupling of Berkes, Liu and Wu [1] to obtain strong approximations for partial sums of dependent sequences. The main tool is a new Rosen-thal type inequality expressed in terms of the coupling coefficients. These coefficients are well suited to some classes of Markov chains or dynamical systems, but they also give new results for smooth functions of linear processes.

The famous results of Koml\'os, Major and Tusn\'ady (see [15] and [17]) state that it is possible to approximate almost surely the partial sums of size n of i.i.d. centered random variables in L p (p > 2) by a Wiener process with an error term of order o(n 1/p). Very recently, Berkes, Liu and Wu [3] extended this famous result to partial sums associated with functions of an i.i.d. sequence, provided a condition on a functional dependence measure in L p is satisfied. In this paper, we adapt the method of Berkes, Liu and Wu to partial sums of functions of random iterates. Taking advantage of the Markovian setting, we shall give new dependent conditions, expressed in terms of a natural coupling (in L $\infty$ or in L 1), under which the strong approximation result holds with rate o(n 1/p). As we shall see our conditions are well adapted to a large variety of models, including left random walks on GL d (R), contracting iterated random functions, autoregressive Lipschitz processes, and some ergodic Markov chains. We also provide some examples showing that our L 1-coupling condition is in some sense optimal.

We give the asymptotic behavior of the Mann-Whitney U-statistic for two independent stationary sequences. The result applies to a large class of short-range dependent sequences, including many non-mixing processes in the sense of Rosenblatt. We also give some partial results in the long-range dependent case, and we investigate other related questions. Based on the theoretical results, we propose some simple corrections of the usual tests for stochastic domination; next we simulate different (non-mixing) stationary processes to see that the corrected tests perform well.

Using martingale methods, we obtain some upper bounds for large and moderate deviations of products of independent and identically distributed elements of GL d (R). We investigate all the possible moment conditions, from super-exponential moments to weak moments of order p \textgreater{} 1, to get a complete picture of the situation. We also prove a moderate deviation principle under an appropriate tail condition.

We consider Markov chains which are polynomially mixing, in a weak sense expressed in terms of the space of functions on which the mixing speed is controlled. In this context, we prove polynomial large and moderate deviations inequalities. These inequalities can be applied in various natural situations coming from probability theory or dynamical systems. Finally, we discuss examples from these various settings showing that our inequalities are sharp.

We study the Lp-integrated risk of some classical estimators of the density, when the observations are drawn from a strictly stationary sequence. The results apply to a large class of sequences, which can be non-mixing in the sense of Rosenblatt and long-range dependent. The main probabilistic tool is a new Rosenthal-type inequality for partial sums of BV functions of the variables. As an application, we give the rates of convergence of regular Histograms, when estimating the invariant density of a class of expanding maps of the unit interval with a neutral fixed point at zero. These Histograms are plotted in the section devoted to the simulations.

Live cell imaging of focal adhesions requires a sufficiently high temporal resolution, which remains a challenging task for super-resolution microscopy. We have addressed this important issue by combining photo-activated localization microscopy (PALM) with super-resolution optical fluctuation imaging (SOFI). Using simulations and fixed cell focal adhesion images, we investigated the complementarity between PALM and SOFI in terms of spatial and temporal resolution. This PALM-SOFI framework was used to image focal adhesions in living cells, while obtaining a temporal resolution below 10 s. We visualized the dynamics of focal adhesions, and revealed local mean velocities around 190 nm per minute. The complementarity of PALM and SOFI was assessed in detail with a methodology that integrates a quantitative resolution and signal-to-noise metric. This PALM and SOFI concept provides an enlarged quantitative imaging framework, allowing unprecedented functional exploration of focal adhesions through the estimation of molecular parameters such as the fluorophore density and the photo-activation and photo-switching rates.