Related papers: Optimal Iterative Threshold-Kernel Estimation of J…
The level set estimation problem seeks to find all points in a domain ${\cal X}$ where the value of an unknown function $f:{\cal X}\rightarrow \mathbb{R}$ exceeds a threshold $\alpha$. The estimation is based on noisy function evaluations…
In this paper, we consider a one-dimensional diffusion process with jumps driven by a Hawkes process. We are interested in the estimations of the volatility function and of the jump function from discrete high-frequency observations in a…
This work investigates the optimal control of the variable-exponent subdiffusion, which extends the work [Gunzburger and Wang, {\it SIAM J. Control Optim.} 2019] to the variable-exponent case to account for the multiscale and crossover…
We propose a new threshold selection method for the nonparametric estimation of the extremal index of stochastic processes. The so-called discrepancy method was proposed as a data-driven smoothing tool for estimation of a probability…
We propose a novel deterministic sampling method to approximate a target distribution $\rho^*$ by minimizing the kernel discrepancy, also known as the Maximum Mean Discrepancy (MMD). By employing the general \emph{energetic variational…
A piecewise-deterministic Markov process is a stochastic process whose behavior is governed by an ordinary differential equation punctuated by random jumps occurring at random times. We focus on the nonparametric estimation problem of the…
This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any…
In extreme value analysis, sensitivity of inference to the definition of extreme event is a paramount issue. Under the peaks-over-threshold (POT) approach, this translates directly into the need of fitting a Generalized Pareto distribution…
We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…
We study a stochastic optimal control problem for jump-diffusion systems whose drift coefficient is piecewise Lipschitz continuous and exhibits threshold-induced discontinuities. Such dynamics naturally arise in applications with…
Several statistical approaches based on reproducing kernels have been proposed to detect abrupt changes arising in the full distribution of the observations and not only in the mean or variance. Some of these approaches enjoy good…
We analyze a solution method for minimization problems over a space of $\mathbb{R}^d$-valued functions of bounded variation on an interval $I$. The presented method relies on piecewise constant iterates. In each iteration the algorithm…
We develop TwinKernel methods for nonparametric estimation of intensity functions of point processes. Building on the general TwinKernel framework and combining it with martingale techniques for counting processes, we construct estimators…
We propose a test for model specification of a parametric diffusion process based on a kernel estimation of the transitional density of the process. The empirical likelihood is used to formulate a statistic, for each kernel smoothing…
Existing drift detection methods focus on designing sensitive test statistics. They treat the detection threshold as a fixed hyperparameter, set once to balance false alarms and late detections, and applied uniformly across all datasets and…
This paper extends the results of the article [C. Kl\"{u}ppelberg and S. M. Pergamenchtchikov. Optimal consumption and investment with bounded downside risk for power utility functions. In Optimality and Risk: {\it Modern Trends in…
Kernel methods for deconvolution have attractive features, and prevail in the literature. However, they have disadvantages, which include the fact that they are usually suitable only for cases where the error distribution is infinitely…
We present a novel approach for the problem of frequency estimation in data streams that is based on optimization and machine learning. Contrary to state-of-the-art streaming frequency estimation algorithms, which heavily rely on random…
Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as…
This paper addresses the problem of approximating an unknown function from point evaluations. When obtaining these point evaluations is costly, minimising the required sample size becomes crucial, and it is unreasonable to reserve a…