Related papers: On the estimation of the convergence rate in the J…
The purpose of this note is to prove a lower bound for the estimation of the memory parameter of a stationary long memory process. The memory parameter is defined here as the index of regular variation of the spectral density at 0. The…
It is now well understood that convex programming can be used to estimate the frequency components of a spectrally sparse signal from $2m+1$ uniform temporal measurements. It is conjectured that a phase transition on the success of the…
Let $f$ be a multivariate density and $f\_n$ be a kernel estimate of $f$ drawn from the $n$-sample $X\_1,...,X\_n$ of i.i.d. random variables with density $f$. We compute the asymptotic rate of convergence towards 0 of the volume of the…
Effective characterisation of the brain grey matter cytoarchitecture with quantitative sensitivity to soma density and volume remains an unsolved challenge in diffusion MRI (dMRI). Solving the problem of relating the dMRI signal with…
Algorithms for the numerical evaluation of the incomplete gamma function ratios $P(a,x)=\gamma(a,x)/\Gamma(a)$ and $Q(a,x)=\Gamma(a,x)/\Gamma(a)$ are described for positive values of $a$ and $x$. Also, inversion methods are given for…
In this paper, we apply a new kind of smoothness concept, i.e. H\"older stability estimates for the determination of convergence rates of Tikhonov regularization for linear and non-linear inverse problems in Hilbert spaces. For linear…
In the present paper, we consider the B\'ezier variant of the general family of Gupta-Srivastava operators \cite{GS:18}. For the proposed operators, we discuss the rate of convergence by using of Lipschitz type space, Ditzian-Totik modulus…
We study the inverse eigenvalue problem for finding doubly stochastic matrices with specified eigenvalues. By making use of a combination of Dykstra's algorithm and an alternating projection process onto a non-convex set, we derive hybrid…
In this paper we present a convergence analysis for the Nystrom method proposed in [Jour. Comput. Phys. 169 pp. 2921-2934, 2001] for the solution of the combined boundary integral equation formulations of sound-soft acoustic scattering…
This paper presents a one-dimensional analog of the Rectangular-Polar (RP) integration strategy and its convergence analysis for weakly singular convolution integrals. The key idea of this method is to break the whole integral into integral…
In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…
We consider LSTD($\lambda$), the least-squares temporal-difference algorithm with eligibility traces algorithm proposed by Boyan (2002). It computes a linear approximation of the value function of a fixed policy in a large Markov Decision…
In this note we construct solutions to rough differential equations ${\rm d} Y = f(Y) \,{\rm d} X$ with a driver $X \in C^\alpha([0,T];\mathbb{R}^d)$, $\frac13 < \alpha \le \frac12$, using a splitting-up scheme. We show convergence of our…
In this paper, some points to the convergence analysis performed in the paper [A new computing approach for power signal modeling using fractional adaptive algorithms, ISA Transactions 68 (2017) 189-202] are presented. It is highlighted…
The spectral density of various ensembles of sparse symmetric random matrices is analyzed using the cavity method. We consider two cases: matrices whose associated graphs are locally tree-like, and sparse covariance matrices. We derive a…
Let $(X_t)_{t \ge 0}$ be solution of a one-dimensional stochastic differential equation. Our aim is to study the convergence rate for the estimation of the invariant density in intermediate regime, assuming that a discrete observation of…
In many machine learning and data related applications, it is required to have the knowledge of approximate ranks of large data matrices at hand. In this paper, we present two computationally inexpensive techniques to estimate the…
We present a Fourier-analytic method for estimating convergence rates in total variation distance in terms of various metrics related to weak convergence. Applications are provided in the areas of Malliavin calculus, normal approximation…
We present an Expectation-Maximization algorithm for the fractal inverse problem: the problem of fitting a fractal model to data. In our setting the fractals are Iterated Function Systems (IFS), with similitudes as the family of…
In this paper, we provide strong $L_2$-rates of approximation of the integral-type functionals of Markov processes by integral sums. We improve the method developed in [2]. Under assumptions on the process formulated only in terms of its…