This paper presents an a posteriori residual error estimator for diffusion-convectionreaction problems approximated by some cell centered finite volume methods on isotropic or anisotropic meshes in Rd, d = 2 or 3. For that purpose we built a reconstructed approximation, which is an appropriate interpolant of the finite volume solution. The error is then the difference between the exact solution...

We focus on the problem of adaptive estimation of signal singularities from indirect and noisy observations. A typical example of such a singularity is a discontinuity (change–point) of the signal or of its derivative. We develop a change–point estimator which adapts to the unknown smoothness of a nuisance deterministic component and to an unknown jump amplitude. We show that the proposed estim...

Numerical causal derivative estimators from noisy data are essential for real time applications especially for control applications or fluid simulation so as to address the new paradigms in solid modeling and video compression. By using an analytical point of view due to Lanczos [9] to this causal case, we revisit n order derivative estimators originally introduced within an algebraic framework...

We propose a simple and general variant of the standard reparameterized gradient estimator for the variational evidence lower bound. Specifically, we remove a part of the total derivative with respect to the variational parameters that corresponds to the score function. Removing this term produces an unbiased gradient estimator whose variance approaches zero as the approximate posterior approac...

We consider a closed Jackson—like queueing network with arbitrary service time distributions and derive an unbiased second derivative estimator of the throughput over N customers served at some node with respect to a parameter of the service distribution at that node. Our approach is based on observing a single sample path of this system, and evaluating all second-order effects on interdepartur...

Optimal bandwidths for local polynomial regression usually involve functionals of the derivatives of the unknown regression function. In the multivariate case, estimates of these functionals are not readily available, primarily because estimating multivariate derivatives is complicated. In this paper, an estimator of multivariate second derivative is obtained via local quadratic regression with...

Abstract: The goal of this paper is to study the bootstrap for the Grenander estimator. The first result is a proof of the inconsistency of the nonparametric bootstrap for the Grenander estimator at a given point. The second result is the development and verification of a bootstrap for the L1 confidence band for the Grenander estimator. As part of this work, kernel estimators are studied as alt...

In the study of stationary stochastic processes on the real line, the covariance function and the spectral density function are parameters of considerable interest. They are equivalent ways of expressing the temporal dependence in the process. In this article, we consider the spectral density function and propose a new estimator that is not based on the periodogram; the estimator is derived thr...

This paper addresses output regulation for nonlinear systems driven by a time varying parameter. The derivative information of the time varying parameter is necessary for the improved regulation performance but it is not readily available in general. In this paper, we propose a velocity estimation of the time varying parameter for use in the control law without amplifying noise signals. key wor...