Related papers: Adaptive thresholding estimation of a Poisson inte…
We consider a doubly stochastic Poisson process with stochastic intensity $\lambda_t =n q\left(X_t\right)$ where $X$ is a continuous It\^o semimartingale and $n$ is an integer. Both processes are observed continuously over a fixed period…
This paper deals with the study of dependencies between two given events modeled by point processes. In particular, we focus on the context of DNA to detect favored or avoided distances between two given motifs along a genome suggesting…
We study the performances of an adaptive procedure based on a convex combination, with data-driven weights, of term-by-term thresholded wavelet estimators. For the bounded regression model, with random uniform design, and the nonparametric…
This paper is devoted to the estimation of the common marginal density function of weakly dependent processes. The accuracy of estimation is measured using pointwise risks. We propose a datadriven procedure using kernel rules. The bandwidth…
Assume that we observe a sample of size n composed of p-dimensional signals, each signal having independent entries drawn from a scaled Poisson distribution with an unknown intensity. We are interested in estimating the sum of the n unknown…
In this work, we propose new matrix- and tensor-based methodologies for estimating multivariate intensity functions of inhomogeneous point processes. By viewing multivariate intensity functions as infinite-dimensional matrices or tensors…
Let $\eta_t$ be a Poisson point process of intensity $t\geq 1$ on some state space $\Y$ and $f$ be a non-negative symmetric function on $\Y^k$ for some $k\geq 1$. Applying $f$ to all $k$-tuples of distinct points of $\eta_t$ generates a…
An adapted, right-continuous, non-decreasing, integer-valued process with unit jumps and starting at zero has a minimal predictable intensity if and only if it is a standard Poisson process under an absolutely continuous transformation of…
We propose an estimation procedure for linear functionals based on Gaussian model selection techniques. We show that the procedure is adaptive, and we give a non asymptotic oracle inequality for the risk of the selected estimator with…
We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. We exhibit a prior on intensities which both leads to a computationally feasible method and enjoys…
We consider the problem of statistical learning for the intensity of a counting process with covariates. In this context, we introduce an empirical risk, and prove risk bounds for the corresponding empirical risk minimizers. Then, we give…
Modelling the first-order intensity function is one of the main aims in point process theory, and it has been approached so far from different perspectives. One appealing model describes the intensity as a function of a spatial covariate.…
In the present paper, we consider the estimation of a periodic two-dimensional function $f(\cdot,\cdot)$ based on observations from its noisy convolution, and convolution kernel $g(\cdot,\cdot)$ unknown. We derive the minimax lower bounds…
Our purpose in this paper is to apply the general methodology for model selection based on T-estimators developed in Birg\'{e} [Ann. Inst. H. Poincar\'{e} Probab. Statist. 42 (2006) 273--325] to the particular situation of the estimation of…
High dimensional Poisson regression has become a standard framework for the analysis of massive counts datasets. In this work we estimate the intensity function of the Poisson regression model by using a dictionary approach, which…
We propose a new estimation procedure of the conditional density for independent and identically distributed data. Our procedure aims at using the data to select a function among arbitrary (at most countable) collections of candidates. By…
The paper considers a Cox process where the stochastic intensity function for the Poisson data model is itself a non-homogeneous Poisson process. We show that it is possible to obtain the marginal data process, namely a non-homogeneous…
Estimating the transition dynamics of controlled Markov chains is crucial in fields such as time series analysis, reinforcement learning, and system exploration. Traditional non-parametric density estimation methods often assume independent…
We propose a data-adaptive probabilistic intensity remapping framework for structure-preserving transformation of grayscale images. The suggested method formulates intensity transformation as a continuous, data-driven remapping process, in…
Given a statistical model, we propose a novel estimation method that yields randomised estimators for the unknown distribution of an observed random variable. We establish non-asymptotic bounds for the performance of these estimators and…