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In this paper we present a frequentist-Bayesian hybrid method for estimating covariances of unfolded distributions using pseudo-experiments. The method is compared with other covariance estimation methods using the unbiased Rao-Cramer bound…

We present a new proof of the quantum Cramer-Rao bound for precision parameter estimation [1-3] and extend it to a more general class of measurement procedures. We analyze a generalized framework for parameter estimation that covers most…

In this paper we derive sharp lower and upper bounds for the covariance of two bounded random variables when knowledge about their expected values, variances or both is available. When only the expected values are known, our result can be…

Estimation of multiple parameters in an unknown Hamiltonian is investigated. We present upper and lower bounds on the time required to complete the estimation within a prescribed tolerance $\delta$. The lower bound is given on the basis of…

It is a common phenomenon that for high-dimensional and nonparametric statistical models, rate-optimal estimators balance squared bias and variance. Although this balancing is widely observed, little is known whether methods exist that…

Shrinkage estimation usually reduces variance at the cost of bias. But when we care only about some parameters of a model, I show that we can reduce variance without incurring bias if we have additional information about the distribution of…

Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…

Artificial neural networks have become important tools to harness the complexity of disordered or random photonic systems. Recent applications include the recovery of information from light that has been scrambled during propagation through…

An adaptive nonparametric estimation procedure is constructed for heteroscedastic regression when the noise variance depends on the unknown regression. A non-asymptotic upper bound for a quadratic risk (oracle inequality) is obtained

The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…

This study proposes a debiasing method for smooth nonparametric estimators. While machine learning techniques such as random forests and neural networks have demonstrated strong predictive performance, their theoretical properties remain…

The Garman-Klass unbiased estimator of the variance per unit time of a zero-drift Brownian Motion B, based on the usual financial data that reports for time windows of equal length the open (OPEN), minimum (MIN), maximum (MAX) and close…

We consider the problem of uncertainty estimation in the context of (non-Bayesian) deep neural classification. In this context, all known methods are based on extracting uncertainty signals from a trained network optimized to solve the…

In random parameter estimation, Bayesian lower bounds (BLBs) for the mean-square error have been noticed to not be tight in a number of cases, even when the sample size, or the signal-to-noise ratio, grow to infinity. In this paper, we…

The problem of covariance estimation for replicated surface-valued processes is examined from the functional data analysis perspective. Considerations of statistical and computational efficiency often compel the use of separability of the…

In modern radar systems, precise target localization using azimuth and velocity estimation is paramount. Traditional unbiased estimation methods have utilized gradient descent algorithms to reach the theoretical limits of the Cramer Rao…

Reinforcement learning methods for robotics are increasingly successful due to the constant development of better policy gradient techniques. A precise (low variance) and accurate (low bias) gradient estimator is crucial to face…

Three classes of stochastic networks and their performance measures are considered. These performance measures are defined as the expected value of some random variables and cannot normally be obtained analytically as functions of network…

When data contains measurement errors, it is necessary to make assumptions relating the observed, erroneous data to the unobserved true phenomena of interest. These assumptions should be justifiable on substantive grounds, but are often…

Practical model building processes are often time-consuming because many different models must be trained and validated. In this paper, we introduce a novel algorithm that can be used for computing the lower and the upper bounds of model…