Related papers: Computational limits to nonparametric estimation f…

The paper deals with the nonparametric estimation problem at a given fixed point for an autoregressive model with unknown distributed noise. Kernel estimate modifications are proposed. Asymptotic minimax and efficiency properties for…

Ergodic optimization aims to single out dynamically invariant Borel probability measures which maximize the integral of a given "performance" function. For a continuous self-map of a compact metric space and a dense set of continuous…

Asymptotic equivalence theory developed in the literature so far are only for bounded loss functions. This limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded. In…

We present a survey of some of our recent results on Bayesian nonparametric inference for a multitude of stochastic processes. The common feature is that the prior distribution in the cases considered is on suitable sets of piecewise…

We study online prediction of bounded stationary ergodic processes. To do so, we consider the setting of prediction of individual sequences and build a deterministic regression tree that performs asymptotically as well as the best…

For a given target density, there exist an infinite number of diffusion processes which are ergodic with respect to this density. As observed in a number of papers, samplers based on nonreversible diffusion processes can significantly…

We consider a bound on the bias reduction of a random number generator by processing based on binary linear codes. We introduce a new bound on the total variation distance of the processed output based on the weight distribution of the code…

Nonparametric estimation of the gap time distribution in a simple renewal process may be considered a problem in survival analysis under particular sampling frames corresponding to how the renewal process is observed. This note describes…

We consider a nonstationary random walk on a compact metrizable abelian group. Under a classical strict aperiodicity assumption we establish a weak-* convergence to the Haar measure, Ergodic Theorem and Large Deviation Type Estimate.

We present a survey of ergodic theorems for actions of algebraic and arithmetic groups recently established by the authors, as well as some of their applications. Our approach is based on spectral methods employing the unitary…

We derive an asymptotic theory of nonparametric estimation for a time series regression model $Z_t=f(X_t)+W_t$, where \ensuremath\{X_t\} and \ensuremath\{Z_t\} are observed nonstationary processes and $\{W_t\}$ is an unobserved stationary…

We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive…

We propose a rigorous decomposition of predictive error, highlighting that not all 'irreducible' error is genuinely immutable. Many domains stand to benefit from iterative enhancements in measurement, construct validity, and modeling. Our…

We initiate the study of effective pointwise ergodic theorems in resource-bounded settings. Classically, the convergence of the ergodic averages for integrable functions can be arbitrarily slow. In contrast, we show that for a class of…

This paper generalizes a part of the theory of $Z$-estimation which has been developed mainly in the context of modern empirical processes to the case of stochastic processes, typically, semimartingales. We present a general theorem to…

We research adaptive maximum likelihood-type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation…

Suppose we observe a geometrically ergodic semi-Markov process and have a parametric model for the transition distribution of the embedded Markov chain, for the conditional distribution of the inter-arrival times, or for both. The first two…

This paper considers an ergodic version of the bounded velocity follower problem, assuming that the decision maker lacks knowledge of the underlying system parameters and must learn them while simultaneously controlling. We propose…

We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…

We propose a novel method for estimating nonseparable selection models. We show that, for a given selection function, the potential outcome distributions are nonparametrically identified from the selected outcome distributions and can be…