Related papers: Some limits to nonparametric estimation for ergodi…

We show uniform convergence of Wiener-Wintner ergodic averages for ergodic actions of (not necessarily countable) locally compact, second countable, abelian (LCA) groups. As a by-product, we obtain a finitary version of the van der Corput…

In the online prediction framework, we use generalized entropy of to study the loss rate of predictors when outcomes are drawn according to stationary ergodic distributions over the binary alphabet. We show that the notion of generalized…

Entropy estimation is a fundamental problem in information theory that has applications in various fields, including physics, biology, and computer science. Estimating the entropy of discrete sequences can be challenging due to limited data…

Let $G$ be a non-periodic amenable group. We prove that there does not exist a topological action of $G$ for which the set of ergodic invariant measures coincides with the set of all ergodic measure-theoretic $G$-systems of entropy zero.…

In this paper, we describe a Bayesian nonparametric approach to make inference for a bivariate spherically symmetric distribution. We consider a Dirichlet invariant process prior on the set of all bivariate spherically symmetric…

We consider the asymptotic behavior of posterior distributions and Bayes estimators based on observations which are required to be neither independent nor identically distributed. We give general results on the rate of convergence of the…

A general notion of bootstrapped $\phi$-divergence estimates constructed by exchangeably weighting sample is introduced. Asymptotic properties of these generalized bootstrapped $\phi$-divergence estimates are obtained, by mean of the…

Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…

This paper deals with a general class of observation-driven time series models with a special focus on time series of counts. We provide conditions under which there exist strict-sense stationary and ergodic versions of such processes. The…

We consider parametric hypotheses testing for multidimensional ergodic diffusion processes observed at discrete time. We propose a family of test statistics, related to the so called $\phi$-divergence measures. By taking into account the…

We propose a nonparametric estimation for a class of fractional stochastic differential equations (FSDE) with random effects. We precisely consider general linear fractional stochastic differential equations with drift depending on random…

We study the existence of algorithms generating almost surely nonnegative unbiased estimators. We show that given a nonconstant real-valued function $f$ and a sequence of unbiased estimators of $\lambda\in\mathbb{R}$, there is no algorithm…

Consider a filtering process associated to a hidden Markov model with densities for which both the state space and the observation space are complete, separable, metric spaces. If the underlying, hidden Markov chain is strongly ergodic and…

One of the most important and useful entropic uncertainty relations concerns a $d$ dimensional system and two mutually unbiased measurements. In such a setting, the sum of two information entropies is lower bounded by $\ln d$. It has…

We propose a nonparametric bootstrap procedure for two-phase stratified sampling without replacement. In this design, a weighted likelihood estimator is known to have smaller asymptotic variance than under the convenient assumption of…

We propose nonparametric identification and semiparametric estimation of joint potential outcome distributions in the presence of confounding. First, in settings with observed confounding, we derive tighter, covariate-informed bounds on the…

We construct multiperiodic processes -- a simple example of stationary ergodic (but not mixing) processes over natural numbers that enjoy the vanishing entropy rate under a mild condition. Multiperiodic processes are supported on randomly…

In the nonparametric regression setting, we construct an estimator which is a continuous function interpolating the data points with high probability, while attaining minimax optimal rates under mean squared risk on the scale of H\"older…

Estimation of a quadratic functional over parameter spaces that are not quadratically convex is considered. It is shown, in contrast to the theory for quadratically convex parameter spaces, that optimal quadratic rules are often rate…

We establish higher-order nonasymptotic expansions for a difference between probability distributions of sums of i.i.d. random vectors in a Euclidean space. The derived bounds are uniform over two classes of sets: the set of all Euclidean…