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Li and Hu recently established variance-type O(1/n) bounds for the sample mean of independent random vectors under sublinear expectations. We extend their results to the exponential concentration regime. For bounded, independent R^d-valued…
This paper is concerned with a rate-distortion theory for sequences of i.i.d. random variables with general distribution supported on general sets including manifolds and fractal sets. Manifold structures are prevalent in data science,…
This paper deals with minimax rates of convergence for estimation of density functions on the real line. The densities are assumed to be location mixtures of normals, a global regularity requirement that creates subtle difficulties for the…
We propose a general framework for regularization in M-estimation problems under time dependent (absolutely regular-mixing) data which encompasses many of the existing estimators. We derive non-asymptotic concentration bounds for the…
Adopting quantum resources for parameter estimation discloses the possibility to realize quantum sensors operating at a sensitivity beyond the standard quantum limit. Such approach promises to reach the fundamental Heisenberg scaling as a…
We give a nearly-optimal algorithm for testing uniformity of distributions supported on $\{-1,1\}^n$, which makes $\tilde O (\sqrt{n}/\varepsilon^2)$ queries to a subcube conditional sampling oracle (Bhattacharyya and Chakraborty (2018)).…
We are interested in the kernel of one-dimensional diffusion equations with continuous coefficients as evaluated by means of explicit discretization schemes of uniform step $h>0$ in the limit as $h\to0$. We consider both semidiscrete…
We consider diffraction at random point scatterers on general discrete point sets in $\R^\nu$, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate the speed of convergence…
Heteroskedasticity testing in nonparametric regression is a classic statistical problem with important practical applications, yet fundamental limits are unknown. Adopting a minimax perspective, this article considers the testing problem in…
Spectral enhancement -- which aims to undo spectral broadening -- leads to integral equations which are ill-posed and require special regularisation techniques for their solution. Even when an optimal regularisation technique is used,…
Sample average approximation (SAA) replaces an intractable expected objective by an empirical average and is a basic device of modern stochastic optimization. We develop a rate theory for optimal values and empirical…
A distributed average consensus algorithm in which every sensor transmits with bounded peak power is proposed. In the presence of communication noise, it is shown that the nodes reach consensus asymptotically to a finite random variable…
We ask to what extent an isolated quantum system can eventually "contract" to be contained within a given Hilbert subspace. We do this by starting with an initial random state, considering the probability that all the particles will be…
This work presents an upper-bound to value that the Kullback-Leibler (KL) divergence can reach for a class of probability distributions called quantum distributions (QD). The aim is to find a distribution $U$ which maximizes the KL…
In this paper we explore the possibility of performing Heisenberg limited quantum metrology of a phase, without any prior, by employing only maximally entangled states. Starting from the estimator introduced by Higgins et al. in New J.…
We consider statistics for stochastic evolution equations in Hilbert space with emphasis on stochastic partial differential equations (SPDEs). We observe a solution process under additional measurement errors and want to estimate a real or…
Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
Multi-layer feedforward networks have been used to approximate a wide range of nonlinear functions. An important and fundamental problem is to understand the learnability of a network model through its statistical risk, or the expected…
In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…