Related papers: Exact local Whittle estimation of fractional integ…
Numerical solutions to fractional differential equations can be extremely computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In finite difference…
When split conformal prediction operates in batch mode with exchangeable data, we determine the exact distribution of the empirical coverage of prediction sets produced for a finite batch of future observables, as well as the exact…
Most of the existing methods for estimating the local intrinsic dimension of a data distribution do not scale well to high-dimensional data. Many of them rely on a non-parametric nearest neighbors approach which suffers from the curse of…
This paper develops the first online algorithms for estimating the spectral density function -- a fundamental object of interest in time series analysis -- that satisfies the three core requirements of streaming inference: fixed memory,…
This paper presents $whittlehurst$, a Python package implementing Whittle's likelihood method for estimating the Hurst exponent in fractional Brownian motion (fBm). While the theoretical foundations of Whittle's estimator are…
Conformal methods create prediction bands that control average coverage assuming solely i.i.d. data. Although the literature has mostly focused on prediction intervals, more general regions can often better represent uncertainty. For…
A novel IV estimation method, that we term Locally Trimmed LS (LTLS), is developed which yields estimators with (mixed) Gaussian limit distributions in situations where the data may be weakly or strongly persistent. In particular, we allow…
We consider a simple mean reverting diffusion process, with piecewise constant drift and diffusion coefficients, discontinuous at a fixed threshold. We discuss estimation of drift and diffusion parameters from discrete observations of the…
We propose an efficient algorithm for approximate computation of the profile maximum likelihood (PML), a variant of maximum likelihood maximizing the probability of observing a sufficient statistic rather than the empirical sample. The PML…
Texture segmentation constitutes a standard image processing task, crucial to many applications. The present contribution focuses on the particular subset of scale-free textures and its originality resides in the combination of three key…
We study the approximation of certain stochastic integrals with respect to a d-dimensional diffusion by corresponding stochastic integrals with piece-wise constant integrands. In finance this corresponds to replacing a continuously adjusted…
We consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate…
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a filter of reduced dimension, we establish that the conditional…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
This paper proposes a local representation for Empirical Likelihood (EL). EL admits the classical local linear quadratic representation by its likelihood ratio property. A local estimator is derived by using the new representation.…
We prove maximum and comparison principles for fractional discrete derivatives in the integers. Regularity results when the space is a mesh of length $h$, and approximation theorems to the continuous fractional derivatives are shown. When…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
In this paper, we introduce weighted fractional generalized cumulative past entropy of a nonnegative absolutely continuous random variable with bounded support. Various properties of the proposed weighted fractional measure are studied.…
We present a robust algorithm that computes (maximally localized) Wannier functions (WFs) without the need of providing an initial guess. Instead, a suitable starting point is constructed automatically from so-called local orbitals which…
Power spectral densities are often interpreted through ensemble averages and long-time asymptotics. In many experiments, however, only a single finite record is available, so spectral estimators remain broadly distributed and the usual…