Related papers: A Cram\'er-Rao inequality for non differentiable m…

This paper proposes a differentiator for sampled signals with bounded noise and bounded second derivative. It is based on a linear program derived from the available sample information and requires no further tuning beyond the noise and…

We devise a systematic method to determine the Fisher information required for resolving two incoherent point sources with a diffraction-limited linear imaging device. The resulting Cram\'er-Rao bound gives the lowest variance achievable…

We develop and analyze a class of unbiased Monte Carlo estimators for multivariate jump-diffusion processes with state-dependent drift, volatility, jump intensity and jump size. A change of measure argument is used to extend existing…

We develop unbiased implicit variational inference (UIVI), a method that expands the applicability of variational inference by defining an expressive variational family. UIVI considers an implicit variational distribution obtained in a…

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…

Almost sure bounds are established on the uniform error of smoothing spline estimators in nonparametric regression with random designs. Some results of Einmahl and Mason (2005) are used to derive uniform error bounds for the approximation…

We identify a common scheme in several existing algorithms addressing computational problems on linear differential equations with polynomial coefficients. These algorithms reduce to computing a linear relation between vectors obtained as…

In this paper, we consider the nonparametric regression problem with multivariate predictors. We provide a characterization of the degrees of freedom and divergence for estimators of the unknown regression function, which are obtained as…

Existing optimal estimators of nonequilibrium path-ensemble averages are shown to fall within the framework of extended bridge sampling. Using this framework, we derive a general minimal-variance estimator that can combine nonequilibrium…

We use the Cramer-Rao bound to show which short magnetic reversals can be recovered successfully from a magnetic anomaly profile. Using a simple variant of the Vine-Matthews model, we show, in particular, that errors in determining the…

Recently, we have proposed a maximum likelihood iterative algorithm for estimation of the parameters of the Nakagami-m distribution. This technique performs better than state of art estimation techniques for this distribution. This could be…

In Stein's method, the exchangeable pair approach is commonly used to estimate the approximation errors in normal approximation. In this paper, we establish a Cram\'er-type moderate deviation theorem of normal approximation for unbounded…

We study the estimation problem for linear time-invariant (LTI) state-space models with Gaussian excitation of an unknown covariance. We provide non asymptotic lower bounds for the expected estimation error and the mean square estimation…

We establish a Berry--Esseen bound for general multivariate nonlinear statistics by developing a new multivariate-type randomized concentration inequality. The bound is the best possible for many known statistics. As applications,…

We analyse the properties of an unbiased gradient estimator of the ELBO for variational inference, based on the score function method with leave-one-out control variates. We show that this gradient estimator can be obtained using a new…

In this paper, we derive the Cramer-Rao bound (CRB) for joint target position and velocity estimation using an active or passive distributed radar network under more general, and practically occurring, conditions than assumed in previous…

Understanding how much each variable contributes to an outcome is a central question across disciplines. A causal view of explainability is favorable for its ability in uncovering underlying mechanisms and generalizing to new contexts.…

Discrimination measures such as the concordance index and the cumulative-dynamic time-dependent area under the ROC-curve (AUC) are widely used in the medical literature for evaluating the predictive accuracy of a scoring rule which relates…

We describe a compact and reliable method to calculate the Fisher information for the estimation of a dynamical parameter in a continuously measured linear Gaussian quantum system. Unlike previous methods in the literature, which involve…

Velocity estimation is a cornerstone of the recently introduced near-field predictive beamforming. This paper derives the Cramer-Rao bounds (CRBs) for joint radial and transverse velocity estimation within a predictive beamforming framework…