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Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…
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…
Nonparametric identification and maximum likelihood estimation for finite-state hidden Markov models are investigated. We obtain identification of the parameters as well as the order of the Markov chain if the transition probability…
We study the nonparametric covariance estimation of a stationary Gaussian field X observed on a regular lattice. In the time series setting, some procedures like AIC are proved to achieve optimal model selection among autoregressive models.…
In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it…
We consider the nonparametric robust estimation problem for regression models in continuous time with semi-Markov noises. An adaptive model selection procedure is proposed. Under general moment conditions on the noise distribution a sharp…
The problem of astrometry is revisited from the perspective of analyzing the attainability of well-known performance limits (the Cramer-Rao bound) for the estimation of the relative position of light-emitting (usually point-like) sources on…
We consider the nonparametric estimation of an S-shaped regression function. The least squares estimator provides a very natural, tuning-free approach, but results in a non-convex optimisation problem, since the inflection point is unknown.…
We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the…
In this paper, we study first the problem of nonparametric estimation of the stationary density $f$ of a discrete-time Markov chain $(X_i)$. We consider a collection of projection estimators on finite dimensional linear spaces. We select an…
This survey provides an overview of optimal estimation of linear functionals which depend on the unknown values of a stationary stochastic sequence. Based on observations of the sequence without noise as well as observations of the sequence…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
We characterize the performance of the widely-used least-squares estimator in astrometry in terms of a comparison with the Cramer-Rao lower variance bound. In this inference context the performance of the least-squares estimator does not…
We study the quadratic prediction error method -- i.e., nonlinear least squares -- for a class of time-varying parametric predictor models satisfying a certain identifiability condition. While this method is known to asymptotically achieve…
The aim of this paper is to introduce an adaptive penalized estimator for identifying the true reduced parametric model under the sparsity assumption. In particular, we deal with the framework where the unpenalized estimator of the…
In this paper we consider non parametric finite translation mixtures. We prove that all the parameters of the model are identifiable as soon as the matrix that defines the joint distribution of two consecutive latent variables is non…
This paper considers estimation and inference in semiparametric econometric models. Standard procedures estimate the model based on an independence restriction that induces a minimum distance between a joint cumulative distribution function…
The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a stochastic stationary sequence from observations of the sequence in special sets of points is considered. Formulas for…
In this paper, we consider the filtering and smoothing recursions in nonparametric finite state space hidden Markov models (HMMs) when the parameters of the model are unknown and replaced by estimators. We provide an explicit and time…
In this paper, we consider the robust adaptive non parametric estimation problem for the drift coefficient in diffusion processes. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed.…