Related papers: Weak convergence in the functional autoregressive …

We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs…

Functional linear regression analysis aims to model regression relations which include a functional predictor. The analog of the regression parameter vector or matrix in conventional multivariate or multiple-response linear regression…

This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…

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…

In this paper, we present the asymptotic properties of the moment estimator for autoregressive (AR for short) models subject to Markovian changes in regime under the assumption that the errors are uncorrelated but not necessarily…

The space time autoregressive model has been widely applied in science, in areas such as economics, public finance, political science, agricultural economics, environmental studies and transportation analyses. The classical space time…

As large language models advance toward superhuman performance, ensuring their alignment with human values and abilities grows increasingly complex. Weak-to-strong generalization offers a promising approach by leveraging predictions from…

Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…

We consider the problem of predicting a real random variable from a functional explanatory variable. The problem is attacked by mean of nonparametric kernel approach which has been recently adapted to this functional context. We derive…

The purpose of this paper is to prove a weak convergence result for empirical processes indexed in general classes of functions and with an underlying $\alpha$-mixing sequence of random variables. In particular the uniformly boundedness…

Estimating the innovation probability density is an important issue in any regression analysis. This paper focuses on functional autoregressive models. A residual-based kernel estimator is proposed for the innovation density. Asymptotic…

In the field of Markov models for image generation, the main idea is to learn how non-trivial images are gradually destroyed by a trivial forward Markov dynamics over the large time window $[0,t]$ converging towards pure noise for $t \to +…

Convergence rates in spectral regularization methods quantify the approximation error in inverse problems as a function of the noise level or the number of sampling points. Classical strong convergence rate results typically rely on source…

Weak convergence of the empirical copula process indexed by a class of functions is established. Two scenarios are considered in which either some smoothness of these functions or smoothness of the underlying copula function is required. A…

Reversible Markov chains play a central role in stochastic modelling and in algorithms such as Markov chain Monte Carlo (MCMC). Motivated by the fundamental importance of reversibility in classical settings, this paper develops a…

The paradigm of weak-to-strong generalization constitutes the training of a strong AI model on data labeled by a weak AI model, with the goal that the strong model nevertheless outperforms its weak supervisor on the target task of interest.…

Observations which are realizations from some continuous process are frequent in sciences, engineering, economics, and other fields. We consider linear models, with possible random effects, where the responses are random functions in a…

Motivated in part by understanding average case analysis of fundamental algorithms in computer science, and in part by the wide array of network data available over the last decade, a variety of random graph models, with corresponding…

This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental…

We expand our effective framework for weak convergence of measures on the real line by showing that effective convergence in the Prokhorov metric is equivalent to effective weak convergence. In addition, we establish a framework for the…