Related papers: Unbiasedness and Bayes Estimation
In this work we study the relation between the set of symmetric operators and the set of mutually unbiased operators from finite plane geometry point of view. Here symmetric operators are generalization of symmetric informationally complete…
Analogous to the notion of mutually unbiased bases for Hilbert spaces, we consider mutually unbiased unitary bases (MUUB) for the space of operators, $M(d, \mathbb{C})$, acting on such Hilbert spaces. The notion of MUUB reflects the…
We propose and study three confidence intervals (CIs) centered at an estimator that is intentionally biased to reduce mean squared error. The first CI simply uses an unbiased estimator's standard error; compared to centering at the unbiased…
The Bayesian approach to ill-posed operator equations in Hilbert space recently gained attraction. In this context, and when the prior distribution is Gaussian, then two operators play a significant role, the one which governs the operator…
In this short note, we consider the problem of estimating multivariate hypergeometric parameters under squared error loss when side information in aggregated data is available. We use the symmetric multinomial prior to obtain Bayes…
The best linear unbiased estimator (BLUE) is a popular statistical method adopted to combine multiple measurements of the same observable taking into account individual uncertainties and their correlation. The method is unbiased by…
An important challenge in statistical analysis concerns the control of the finite sample bias of estimators. For example, the maximum likelihood estimator has a bias that can result in a significant inferential loss. This problem is…
Motivated by the proliferation of observational datasets and the need to integrate non-randomized evidence with randomized controlled trials, causal inference researchers have recently proposed several new methodologies for combining biased…
Mutually unbiased measurements are a generalization of mutually unbiased bases in which the measurement operators need not to be rank one projectors. In a $d$-dimension space, the purity of measurement elements ranges from $1/d$ for the…
When evaluating and comparing models using leave-one-out cross-validation (LOO-CV), the uncertainty of the estimate is typically assessed using the variance of the sampling distribution. Considering the uncertainty is important, as the…
Measuring incomplete sets of mutually unbiased bases constitutes a sensible approach to the tomography of high-dimensional quantum systems. The unbiased nature of these bases optimizes the uncertainty hypervolume. However, imposing…
We derive mean-unbiased estimators for the structural parameter in instrumental variables models with a single endogenous regressor where the sign of one or more first stage coefficients is known. In the case with a single instrument, there…
In this paper the problem of best linear unbiased estimation is investigated for continuous-time regression models. We prove several general statements concerning the explicit form of the best linear unbiased estimator (BLUE), in particular…
This paper studies nonparametric empirical Bayes methods in a heterogeneous parameters framework that features unknown means and variances. We provide extended Tweedie's formulae that express the (infeasible) optimal estimators of…
Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased…
In empirical research, when we have multiple estimators for the same parameter of interest, a central question arises: how do we combine unbiased but less precise estimators with biased but more precise ones to improve the inference? Under…
We derive a maximum a posteriori estimator for the linear observation model, where the signal and noise covariance matrices are both uncertain. The uncertainties are treated probabilistically by modeling the covariance matrices with prior…
We address the problem of existence of unbiased constrained parameter estimators. We show that if the constrained set of parameters is compact and the hypothesized distributions are absolutely continuous with respect to one another, then…
In this paper, we consider the extent of the biases that may arise when an unmeasured confounder is omitted from a structural equation model (SEM) and we propose sensitivity analysis techniques to correct for such biases. We give an…
We define a left quotient as well as a right quotient of two bounded operators between Hilbert spaces, and we parametrize these two concepts using the Moore-Penrose inverse. In particular, we show that the adjoint of a left quotient is a…