Related papers: Estimation Error: Distribution and Pointwise Limit…
The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…
We examine the theoretical properties of the index of agreement loss function $L_W$, the negatively oriented counterpart of Willmott's index of agreement, a common metric in environmental sciences and engineering. We prove that $L_W$ is…
The Gaussian theory of errors has been generalized to situations, where the Gaussian distribution and, hence, the Gaussian rules of error propagation are inadequate. The generalizations are based on Bayes' theorem and a suitable measure.…
This paper considers the problem of recovering the permutation of an n-dimensional random vector X observed in Gaussian noise. First, a general expression for the probability of error is derived when a linear decoder (i.e., linear estimator…
It was recently proposed to encode the one-sided exponential source X via K parallel channels, Y1, ..., YK , such that the error signals X - Yi, i = 1,...,K, are one-sided exponential and mutually independent given X. Moreover, it was shown…
We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on $(0,\infty)$. For the maximum likelihood (ML) estimator and…
In many radar scenarios, the radar target or the medium is assumed to possess randomly varying parts. The properties of a target are described by a random process known as the spreading function. Its second order statistics under the WSSUS…
The directional precision of the sample mean estimator was calculated analytically for the offset exponential and normal distributions in three-dimensional space both for a finite sample and for limiting cases. It was shown that the…
The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In…
Causal inference requires evaluating models on balanced distributions between treatment and control groups, while training data often exhibits imbalance due to historical decision-making policies. Most conventional statistical methods…
We construct an efficient estimator for the error distribution function of the nonparametric regression model Y = r(Z) + e. Our estimator is a kernel smoothed empirical distribution function based on residuals from an under-smoothed local…
We provide the first proof of convergence for normalized error feedback algorithms across a wide range of machine learning problems. Despite their popularity and efficiency in training deep neural networks, traditional analyses of error…
We consider the regression model with errors-in-variables where we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f(X)+\xi, Z=X+\sigma\epsilon$, involving independent and unobserved random variables $X,\xi,\epsilon$. The density $g$ of…
In this paper several related estimation problems are addressed from a Bayesian point of view and optimal estimators are obtained for each of them when some natural loss functions are considered. Namely, we are interested in estimating a…
While significant progress has been made in specifying neural networks capable of representing uncertainty, deep networks still often suffer from overconfidence and misaligned predictive distributions. Existing approaches for measuring this…
Signal processing makes extensive use of point estimators and accompanying error bounds. These work well up until the likelihood function has two or more high peaks. When it is important for an estimator to remain reliable, it becomes…
This paper studies the prediction of a target $\mathbf{z}$ from a pair of random variables $(\mathbf{x},\mathbf{y})$, where the ground-truth predictor is additive $\mathbb{E}[\mathbf{z} \mid \mathbf{x},\mathbf{y}] = f_\star(\mathbf{x})…
Given the unconfoundedness assumption, we propose new nonparametric estimators for the reduced dimensional conditional average treatment effect (CATE) function. In the first stage, the nuisance functions necessary for identifying CATE are…
This dissertation shows that careful injection of noise into sample data can substantially speed up Expectation-Maximization algorithms. Expectation-Maximization algorithms are a class of iterative algorithms for extracting maximum…
We study an estimator for smoothing irregularly sampled data into a smooth map. The estimator has been widely used in astronomy, owing to its low level of noise; it involves a weight function -- or smoothing kernel -- w(\theta). We show…