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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 propose a rectangular rotational invariant estimator to recover a real matrix from noisy matrix observations coming from an arbitrary additive rotational invariant perturbation, in the large dimension limit. Using the Bayes-optimality of…
We investigate asymptotic inference in a linear regression model where both response and regressors are functions, using an estimator based on functional principal components analysis. Although this approach is widely used in functional…
This study presents a Bayesian maximum \textit{a~posteriori} (MAP) framework for dynamical system identification from time-series data. This is shown to be equivalent to a generalized Tikhonov regularization, providing a rational…
The large-system performance of MAP estimation is studied considering a general distortion function when the observation vector is received through a linear system with additive white Gaussian noise. The analysis considers the system matrix…
This paper obtains asymptotic results for parametric inference using prediction-based estimating functions when the data are high frequency observations of a diffusion process with an infinite time horizon. Specifically, the data are…
Violation of the assumptions underlying classical (Gaussian) limit theory often yields unreliable statistical inference. This paper shows that the bootstrap can detect such violations by delivering simple and powerful diagnostic tests that…
We study the problem of estimating the mode and maximum of an unknown regression function in the presence of noise. We adopt the Bayesian approach by using tensor-product B-splines and endowing the coefficients with Gaussian priors. In the…
In the problem of selecting variables in a multivariate linear regression model, we derive new Bayesian information criteria based on a prior mixing a smooth distribution and a delta distribution. Each of them can be interpreted as a fusion…
This paper proposes a new Bayesian strategy for the smooth estimation of altimetric parameters. The altimetric signal is assumed to be corrupted by a thermal and speckle noise distributed according to an independent and non identically…
In this paper we study the asymptotics of linear regression in settings with non-Gaussian covariates where the covariates exhibit a linear dependency structure, departing from the standard assumption of independence. We model the covariates…
In this paper we construct optimal designs for frequentist model averaging estimation. We derive the asymptotic distribution of the model averaging estimate with fixed weights in the case where the competing models are non-nested and none…
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncertain. These parametric quantities are then identified by…
Predictive mean matching imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the predictive mean matching estimator of the population mean. For variance estimation,…
We prove the strong consistency and the asymptotic normality of the maximum likelihood estimator of the parameters of a general conditionally heteroscedastic model with $\alpha$-stable innovations. Then, we relax the assumptions and only…
In this paper, we consider the usual linear regression model in the case where the error process is assumed strictly stationary. We use a result from Hannan, who proved a Central Limit Theorem for the usual least squares estimator under…
In this note we consider the finite-dimensional parameter estimation problem associated to inverse problems. In such scenarios, one seeks to maximize the marginal likelihood associated to a Bayesian model. This latter model is connected to…
While learning the maximum likelihood value of parameters of an undirected graphical model is hard, modelling the posterior distribution over parameters given data is harder. Yet, undirected models are ubiquitous in computer vision and text…
This paper discusses asymptotic distributions of various estimators of the underlying parameters in some regression models with long memory (LM) Gaussian design and nonparametric heteroscedastic LM moving average errors. In the simple…
We recapitulate the Bayesian formulation of neural network based classifiers and show that, while sampling from the posterior does indeed lead to better generalisation than is obtained by standard optimisation of the cost function, even…