Related papers: Some limits to nonparametric estimation for ergodi…

A new negative result for nonparametric estimation of binary ergodic processes is shown. I The problem of estimation of distribution with any degree of accuracy is studied. Then it is shown that for any countable class of estimators there…

We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…

The problem of prediction consists in forecasting the conditional distribution of the next outcome given the past. Assume that the source generating the data is such that there is a stationary ergodic predictor whose error converges to zero…

In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable- and…

We proposed a learning algorithm for nonparametric estimation and on-line prediction for general stationary ergodic sources. We prepare histograms each of which estimates the probability as a finite distribution, and mixture them with…

We investigate the moment estimation for an ergodic diffusion process with unknown trend coefficient. We consider nonparametric and parametric estimation. In each case, we present a lower bound for the risk and then construct an…

This paper presents several situations leading to the observation of multiple correlated copies of a drifted process, and then non-asymptotic risk bounds are established on nonparametric estimators of the drift function $b_0$ and its…

In this work a method for statistical analysis of time series is proposed, which is used to obtain solutions to some classical problems of mathematical statistics under the only assumption that the process generating the data is stationary…

A problem of improving the accuracy of nonparametric entropy estimation for a stationary ergodic process is considered. New weak metrics are introduced and relations between metrics, measures, and entropy are discussed. Based on weak…

In this paper we consider the nonparametric estimation of density and regression functions with non-negative support using a gamma kernel procedure introduced by Chen (2000). Strong uniform consistency and asymptotic normality of the…

We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a…

This paper is concerned with nonparametric estimation of the weighted stochastic block model. We first show that the model implies a set of multilinear restrictions on the joint distribution of edge weights of certain subgraphs involving…

Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…

For probability measures on countable spaces we derive distributional limits for empirical entropic optimal transport quantities. More precisely, we show that the empirical optimal transport plan weakly converges to a centered Gaussian…

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…

We consider the problem of estimating the context tree of a stationary ergodic process with finite alphabet without imposing additional conditions on the process. As a starting point we introduce a Hamming metric in the space of irreducible…

We consider the problems of parameter estimation for several models of threshold ergodic diffusion processes in the asymptotics of large samples. These models are the direct continuous time analogues of the well-known in time series…

We consider the question of estimating the drift and the invariant density for a large class of scalar ergodic diffusion processes, based on continuous observations, in $\sup$-norm loss. The unknown drift $b$ is supposed to belong to a…

We study asymptotic behaviors of Bayes type estimators and give sufficient conditions to obtain asymptotic limit distribution of estimation error. We assume polynomial type large deviation inequalities and prove asymptotic equivalence of…

We address the problem of nonparametric estimation of characteristics for stationary and ergodic time series. We consider finite-alphabet time series and real-valued ones and the following four problems: i) estimation of the (limiting)…