Fabienne Comte
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View article: Nonparametric Estimation in SDE Models Involving an Explanatory Process
Nonparametric Estimation in SDE Models Involving an Explanatory Process Open
This paper deals with the process $X = (X_t)_{t\in [0,T]}$ defined by the stochastic differential equation (SDE) $dX_t = (a(X_t) + b(Y_t))dt +σ(X_t)dW_1(t)$, where $W_1$ is a Brownian motion and $Y$ is an exogenous process. The first task …
View article: Estimating the intensity of a filtered Poisson point process on Rd
Estimating the intensity of a filtered Poisson point process on Rd Open
Motivated by the preeminence of Poisson point processes in various imaging modalities, we address the problem of recovering the intensity of a filtered Poisson point process on R d . That is, we observe the convolution of the measure µ und…
View article: Non parametric regression function estimation in presence of common noise
Non parametric regression function estimation in presence of common noise Open
Consider the regression model (Yi = b(Xi) + ui, i = 1, . . . , n) with error process ui = √ ρε0 + √ 1 -ρεi where (εi, i = 0, . . . , n) are independent centered random variables (r.v.) with unit variance and (X1, . . . , Xn) are independen…
View article: Nonparametric estimation of the transition density function for diffusion processes
Nonparametric estimation of the transition density function for diffusion processes Open
International audience
View article: Estimation for the convolution of several multidimensional densities
Estimation for the convolution of several multidimensional densities Open
This work is concerned with the problem of estimating the m-fold convolution of the densities of m independent random vectors. Two nonparametric estimators are proposed, a kernel and a projection estimator, and their integrated quadratic r…
View article: Nonparametric moment method for scalar McKean–Vlasov stochastic differential equations
Nonparametric moment method for scalar McKean–Vlasov stochastic differential equations Open
We study the nonparametric estimation of both the potential and the interaction terms of a scalar McKean–Vlasov stochastic differential equation (SDE) in stationary regime from a continuous observation on a time interval [0, T ], with asym…
View article: Quadratic functional estimation from observations with multiplicative measurement error
Quadratic functional estimation from observations with multiplicative measurement error Open
We consider the nonparametric estimation of the value of a quadratic functional evaluated at the density of a strictly positive random variable $X$ based on an iid. sample from an observation $Y$ of $X$ corrupted by an independent multipli…
View article: Nonparametric Estimation of the Transition Density Function for Diffusion Processes
Nonparametric Estimation of the Transition Density Function for Diffusion Processes Open
We assume that we observe $N$ independent copies of a diffusion process on a time-interval $[0,2T]$. For a given time $t$, we estimate the transition density $p_t(x,y)$, namely the conditional density of $X_{t + s}$ given $X_s = x$, under …
View article: Nonparametric estimation for i.i.d. stochastic differential equations with space-time dependent coefficients
Nonparametric estimation for i.i.d. stochastic differential equations with space-time dependent coefficients Open
We consider N i.i.d. one-dimensional inhomogeneous diusion processes (X_i(t), i = 1,. .. , N) with drift µ(t, x) = \sum_{ j=1}^K \alpha_jj(t)g_j(x) and diffusion coefficient σ(t, x), where K, the functions g_j(x) and σ(t, x) are known. Our…
View article: Nonparametric adaptive estimation for interacting particle systems
Nonparametric adaptive estimation for interacting particle systems Open
We consider a stochastic system of interacting particles with constant diffusion coefficient and drift linear in space, time‐depending on two unknown deterministic functions. Our concern here is the nonparametric estimation of these functi…
View article: On a projection estimator of the regression function derivative
On a projection estimator of the regression function derivative Open
In this paper, we study the estimation of the derivative of a regression function in a standard univariate regression model. The estimators are defined either by derivating nonparametric least-squares estimators of the regression function …
View article: Should we estimate a product of density functions by a product of estimators?
Should we estimate a product of density functions by a product of estimators? Open
International audience
View article: Nonparametric Drift Estimation from Diffusions with Correlated Brownian Motions
Nonparametric Drift Estimation from Diffusions with Correlated Brownian Motions Open
In the present paper, we consider that $N$ diffusion processes $X^1,\dots,X^N$ are observed on $[0,T]$, where $T$ is fixed and $N$ grows to infinity. Contrary to most of the recent works, we no longer assume that the processes are independ…
View article: Linear functional estimation under multiplicative measurement errors
Linear functional estimation under multiplicative measurement errors Open
We study the non-parametric estimation of the value $θ(f )$ of a linear functional evaluated at an unknown density function f with support on $R_+$ based on an i.i.d. sample with multiplicative measurement errors. The proposed estimation p…
View article: On a Projection Estimator of the Regression Function Derivative
On a Projection Estimator of the Regression Function Derivative Open
In this paper, we study the estimation of the derivative of a regression function in a standard univariate regression model. The estimators are defined either by derivating nonparametric least-squares estimators of the regression function …
View article: Hazard regression with noncompactly supported bases
Hazard regression with noncompactly supported bases Open
In this article, we consider the problem of nonparametric hazard rate estimation in the presence of right‐censored observations. We provide a generalized risk bound for a regression‐type nonparametric estimator of the hazard function of in…
View article: On a Nadaraya-Watson estimator with two bandwidths
On a Nadaraya-Watson estimator with two bandwidths Open
In a regression model, we write the Nadaraya-Watson estimator of the regression function as the quotient of two kernel estimators, and propose a bandwidth selection method for both the numerator and the denominator. We prove risk bounds fo…
View article: Kernel estimation for Lévy driven stochastic convolutions
Kernel estimation for Lévy driven stochastic convolutions Open
We consider a Lévy driven stochastic convolution, also called continuous time Lévy driven moving average model X ( t ) = ∫ 0 t a ( t - s ) d Z ( s ) X(t)=\int_{0}^{t}a(t-s)\,dZ(s) , where 𝑍 is a Lévy martingal…
View article: Spectral cut-off regularisation for density estimation under multiplicative measurement errors
Spectral cut-off regularisation for density estimation under multiplicative measurement errors Open
We study the non-parametric estimation of an unknown density f with support on R+ based on an i.i.d. sample with multiplicative measurement errors. The proposed fully data driven procedure is based on the estimation of the Mellin transform…
View article: Nonparametric drift estimation for i.i.d. paths of stochastic differential equations
Nonparametric drift estimation for i.i.d. paths of stochastic differential equations Open
We consider $N$ independent stochastic processes $(X_{i}(t),t\\in [0,T])$, $i=1,\\ldots ,N$, defined by a one-dimensional stochastic differential equation, which are continuously observed throughout a time interval $[0,T]$ where $T$ is fix…
View article: Spectral cut-off regularisation for density estimation under\n multiplicative measurement errors
Spectral cut-off regularisation for density estimation under\n multiplicative measurement errors Open
We study the non-parametric estimation of an unknown density f with support\non R+ based on an i.i.d. sample with multiplicative measurement errors. The\nproposed fully data driven procedure is based on the estimation of the Mellin\ntransf…