Related papers: Adaptive thresholding estimation of a Poisson inte…
In this paper, we study the minimax rates and provide an implementable convex algorithm for Poisson inverse problems under weak sparsity and physical constraints. In particular we assume the model $y_i \sim \mbox{Poisson}(Ta_i^{\top}f^*)$…
We consider non-parametric estimation problems in the presence of dependent data, notably non-parametric regression with random design and non-parametric density estimation. The proposed estimation procedure is based on a dimension…
We consider the estimation of a structural function which models a non-parametric relationship between a response and an endogenous regressor given an instrument in presence of dependence in the data generating process. Assuming an…
A new multivariate density estimator for stationary sequences is obtained by Fourier inversion of the thresholded empirical characteristic function. This estimator does not depend on the choice of parameters related to the smoothness of the…
Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…
The intensity of a Gibbs point process is usually an intractable function of the model parameters. For repulsive pairwise interaction point processes, this intensity can be expressed as the Laplace transform of some particular function.…
We consider the regression model with (known) random design. We investigate the minimax performances of an adaptive wavelet block thresholding estimator under the $\mathbb{L}^p$ risk with $p\ge 2$ over Besov balls. We prove that it is near…
We present the Additive Poisson Process (APP), a novel framework that can model the higher-order interaction effects of the intensity functions in stochastic processes using lower dimensional projections. Our model combines the techniques…
In this paper, we study the nonparametric maximum likelihood estimator for an event time distribution function at a point in the current status model with observation times supported on a grid of potentially unknown sparsity and with…
In this thesis we study adaptive nonparametric regression with noise misspecification and the complexity of approximation of random fields in dependence of the dimension. First, we consider the problem of pointwise estimation in…
We study systems of simple point processes that admit stochastic intensities. We represent these point processes as thinnings of Poisson measures and are interested in a convergence result of such systems. This result states that, if the…
Let $\sigma$ be a non-atomic, infinite Radon measure on $\mathbb R^d$, for example, $d\sigma(x)=z\,dx$ where $z>0$. We consider a system of freely independent particles $x_1,\dots,x_N$ in a bounded set $\Lambda\subset\mathbb R^d$, where…
In this paper we provide theoretical support for the so-called "Sigmoidal Gaussian Cox Process" approach to learning the intensity of an inhomogeneous Poisson process on a $d$-dimensional domain. This method was proposed by Adams, Murray…
This paper studies theory and inference of an observation-driven model for time series of counts. It is assumed that the observations follow a Poisson distribution conditioned on an accompanying intensity process, which is equipped with a…
The inefficiency of using an unbiased estimator in a Monte Carlo procedure can be quantified using an inefficiency constant, equal to the product of the variance of the estimator and its mean computational cost. We develop methods for…
We consider the problem of the estimation of the mean function of an inhomogeneous Poisson process when its intensity function is periodic. For the mean integrated squared error (MISE) there is a classical lower bound for all estimators and…
In this paper, we consider parameter estimation for stochastic differential equations driven by Wiener processes and compound Poisson processes. We assume unknown parameters corresponding to coefficients of the drift term, diffusion term,…
Several classical adaptive optimization algorithms, such as line search and trust region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic…
The authors consider the problem of estimating the density $g$ of independent and identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$, $\epsilon$ is a noise…
The observations in many applications consist of counts of discrete events, such as photons hitting a detector, which cannot be effectively modeled using an additive bounded or Gaussian noise model, and instead require a Poisson noise…