Related papers: Unbiasedness and Bayes Estimation
The efficiency of two Bayesian order estimators is studied. By using nonparametric techniques, we prove new underestimation and overestimation bounds. The results apply to various models, including mixture models. In this case, the errors…
This paper is mainly concerned with proving $\sigma(AB)=\sigma(BA)$ for two linear and non necessarily bounded operators $A$ and $B$. The main tool is left and right invertibility of bounded and unbounded operators.
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
Causal inference methods have been applied in various fields where researchers want to estimate treatment effects. In traditional causal inference settings, one assumes that the outcome of a unit does not depend on treatments of other…
Two equivalent ways of looking for mutually unbiased bases are discussed in this note. The passage from the search for d+1 mutually unbiased bases in C(d) to the search for d(d+1) vectors in C(d*d) satisfying constraint relations is…
We propose a rigorous, non-perturbative, Bayesian framework which enables one jointly to test Gaussianity and estimate the power spectrum of CMB anisotropies. It makes use of the Hilbert space of an harmonic oscillator to set up an exact…
For bounded linear operators $A,B$ on a Hilbert space $\mathcal{H}$ we show the validity of the estimate $$ \sum_{\lambda \in \sigma_d (B)} \dist(\lambda, \overline{\num}(A))^p \leq \| B-A \|_{\mathcal{S}_p}^p$$ and apply it to recover and…
The recent thought-provoking paper by Hansen [2022, Econometrica] proved that the Gauss-Markov theorem continues to hold without the requirement that competing estimators are linear in the vector of outcomes. Despite the elegant proof, it…
We study methods for simultaneous analysis of many noisy and biased estimates, each paired with an even noisier estimate of its own bias. The analyst's goal is to construct short calibrated intervals for each parameter. The standard…
Due to the potential benefits of parallelization, designing unbiased Monte Carlo estimators, primarily in the setting of randomized multilevel Monte Carlo, has recently become very popular in operations research and computational…
In this article, we consider computing expectations w.r.t. probability measures which are subject to discretization error. Examples include partially observed diffusion processes or inverse problems, where one may have to discretize time…
This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator.…
Unbiased estimators are introduced for averaged Bregman divergences which generalize Stein's Unbiased (Predictive) Risk Estimator, and the minimization of these estimators is proposed as a regularization parameter selection method for…
Large datasets are often affected by cell-wise outliers in the form of missing or erroneous data. However, discarding any samples containing outliers may result in a dataset that is too small to accurately estimate the covariance matrix.…
We propose a principled framework for nonparametric empirical Bayes (EB) estimation, based on the idea that the prior should be consistent with the observed posterior and that Bayesian updating should be stable. Focusing on discretized…
We study the entanglement detection by using mutually unbiased measurements and provide a quantum separability criterion that can be experimentally implemented for arbitrary $d$-dimensional bipartite systems. We show that this criterion is…
We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…
On a variety of complex decision-making tasks, from doctors prescribing treatment to judges setting bail, machine learning algorithms have been shown to outperform expert human judgments. One complication, however, is that it is often…
For analyzing unit-level multivariate data in small area estimation, we consider the multivariate nested error regression model (MNER) and provide the empirical best linear unbiased predictor (EBLUP) of a small area characteristic based on…
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…