Abstract: In this paper, we study the following model of hidden Markov chain: Yi = Xi + εi, i = 1, . . . , n + 1 with (Xi) a real-valued stationary Markov chain and (εi)1≤i≤n+1 a noise having a known distribution and independent of the sequence (Xi). We present an estimator of the transition density obtained by minimization of an original contrast that takes advantage of the regressive aspect o...

We investigate the empirical Bayes estimation problem of multivariate regression coefficients under squared error loss function. In particular, we consider the regression model Y = Xβ+ ε, where Y is an m-vector of observations, X is a known m× k matrix, β is an unknown k-vector, and ε is anm-vector of unobservable random variables. The problem is squared error loss estimation of β based on some...

Let q ∈ (1, 2) and x ∈ [0, 1 q−1 ]. We say that a sequence (εi) ∞ i=1 ∈ {0, 1}N is an expansion of x in base q (or a q-expansion) if

This Note presents original rates of convergence for the deconvolution problem. We assume that both the estimated density and noise density are supersmooth and we compute the risk for two kinds of estimators. Résumé Vitesses de convergence en déconvolution nonparamétrique. Cette Note présente des vitesses de convergence originales pour le problème de déconvolution. On suppose que la densité est...

Yi = f(xi) + εi = g(Θ >xi) + εi, i = 1, . . . , n, is addressed. In the general setup we are interested in, the covariates xi ∈ R, Θ is a d×m orthogonal matrix (ΘΘ = Im∗) and g : R ∗ → R is an unknown function. To be able to estimate Π consistently, we assume that S = Im(Θ) is the smallest subspace satisfying f(xi) = f(ΠSxi), ∀i = 1, . . . , n, where ΠS stands for the orthogonal projector in R ...

1 Markov Random Field Model The following section will outline the mathematical model in our contact prediction method that is essentially identical to the plmDCA (Ekeberg et al., 2013) and GREMLIN (Kamisetty et al., 2013) methods. We eliminate transitive interactions in the observed interaction network by learning a generative model of the MSA using a Markov Random Field (MRF). Assuming we hav...

In the convolution model Zi = Xi + εi, we give a model selection procedure to estimate the density of the unobserved variables (Xi) 1≤i≤n , when the sequence (Xi) i≥1 is strictly stationary but not necessarily independent. This procedure depends on wether the density of εi is super smooth or ordinary smooth. The rates of convergence of the penalized contrast estimators are the same as in the in...

In statistical physics textbooks, one often encounters systems which consist of macroscopic numbers of identical small parts which do not interact with each other. This is not too unrealistic since there are many physical systems (such as certain spin systems, including nuclear spin systems) which are well approximated by such non-interacting models in some ranges of temperature and time. The q...

We consider a general framework to study the evolution of wage and earnings residuals that incorporates features highlighted by two influential but distinct literatures in economics: (i) unobserved skills with changing non-linear pricing functions and (ii) idiosyncratic shocks that follow a rich stochastic process. Specifically, we consider residuals for individual i in period t of the form: Wi...

This paper corrects the statement and the proof of Theorem 1.5 of the paper quoted in the title (Represent. Theory 13 (2009), 427–459). Theorem 1.5 of our paper [1] requires a correction. Below we provide a new statement of this theorem and correct the proof. A mistake in the original proof of Theorem 1.5 is due to missing the multiple 2 at a certain point of the proof (see [1, page 456, line 2...