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In the analysis of cluster data, the regression coefficients are frequently assumed to be the same across all clusters. This hampers the ability to study the varying impacts of factors on each cluster. In this paper, a semiparametric model…

We study the problem of learning clusters of partially observed linear dynamical systems from multiple input-output trajectories. This setting is particularly relevant when there are limited observations (e.g., short trajectories) from…

Multifractal analysis of multiplicative random cascades is revisited within the framework of {\em mixed asymptotics}. In this new framework, statistics are estimated over a sample which size increases as the resolution scale (or the…

We consider a discrete-time model for random interface growth which admits exact formulas and converges to the Polynuclear growth model in a particular limit. The height of the interface is initially flat and the evolution involves the…

We prove clustering estimates for the truncated correlations, i.e., cumulants of an unbounded spin system on the lattice. We provide a unified treatment, based on cluster expansion techniques, of four different regimes: large mass, small…

An approach for understanding the behavior of multiplicity distributions in restricted phase-space intervals derived on the basis of global observables is proposed. We obtain a unifying connection between local multiparticle clusters and…

The rate of metastable decay in nonequilibrium systems is expected to display scaling behavior: i.e., the logarithm of the decay rate should scale as a power of the distance to a bifurcation point where the metastable state disappears.…

We establish the asymptotic expansion in $\beta$ matrix models with a confining, off-critical potential, in the regime where the support of the equilibrium measure is a union of segments. We first address the case where the filling…

When data are clustered, common practice has become to do OLS and use an estimator of the covariance matrix of the OLS estimator that comes close to unbiasedness. In this paper we derive an estimator that is unbiased when the random-effects…

We introduce a trimmed version of the Hill estimator for the index of a heavy-tailed distribution, which is robust to perturbations in the extreme order statistics. In the ideal Pareto setting, the estimator is essentially finite-sample…

We investigate the estimation of multivariate extreme models with a discrete spectral measure using spherical clustering techniques. The primary contribution involves devising a method for selecting the order, that is, the number of…

We discuss the asymptotic behaviour of models of lattice polygons, mainly on the square lattice. In particular, we focus on limiting area laws in the uniform perimeter ensemble where, for fixed perimeter, each polygon of a given area occurs…

Clustering is a popular unsupervised learning tool often used to discover groups within a larger population such as customer segments, or patient subtypes. However, despite its use as a tool for subgroup discovery and description - few…

We study statistical inference for small-noise-perturbed multiscale dynamical systems under the assumption that we observe a single time series from the slow process only. We construct estimators for both averaging and homogenization…

We consider a random interval splitting process, in which the splitting rule depends on the empirical distribution of interval lengths. We show that this empirical distribution converges to a limit almost surely as the number of intervals…

We investigate the theoretical performances of the Partial Least Square (PLS) algorithm in a high dimensional context. We provide upper bounds on the risk in prediction for the statistical linear model when considering the PLS estimator.…

When analysing extreme values, two alternative statistical approaches have historically been held in contention: the block maxima method (or annual maxima method, spurred by hydrological applications) and the peaks-over-threshold. Clamoured…

Random walkers absorbing on a boundary sample the Harmonic Measure linearly and independently: we discuss how the recurrence times between impacts enable non-linear moments of the measure to be estimated. From this we derive a new technique…

Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…

The extremal index parameter theta characterizes the degree of local dependence in the extremes of a stationary time series and has important applications in a number of areas, such as hydrology, telecommunications, finance and…