Related papers: What Estimators Are Unbiased For Linear Models?

Although unbiasedness is a basic property of a good test, many tests on vector parameters or scalar parameters against two-sided alternatives are not finite-sample unbiased. This was already noticed by Sugiura [Ann. Inst. Statist. Math. 17…

This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not…

The Barankin bound is generalized to the vector case in the mean square error sense. Necessary and sufficient conditions are obtained to achieve the lower bound. To obtain the result, a simple finite dimensional real vector valued…

We study causal effect estimation from a mixture of observational and interventional data in a confounded linear regression model with multivariate treatments. We show that the statistical efficiency in terms of expected squared error can…

Precision matrix estimation is a cornerstone concept in statistics, economics, and finance. Despite advances in recent years, estimation methods that are simultaneously (i) dense, (ii) consistent, and (iii) model-free are lacking. While…

This paper proposes a debiased estimator for causal effects in high-dimensional generalized linear models with binary outcomes and general link functions. The estimator augments a regularized regression plug-in with weights computed from a…

This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…

Many estimators of the variance of the well-known unbiased and uniform most powerful estimator $\htheta$ of the Mann-Whitney effect, $\theta = P(X < Y) + \nfrac12 P(X=Y)$, are considered in the literature. Some of these estimators are only…

In a smooth semiparametric estimation problem, the marginal posterior for the parameter of interest is expected to be asymptotically normal and satisfy frequentist criteria of optimality if the model is endowed with a suitable prior. It is…

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 study in this paper lower bounds for the generalization error of models derived from multi-layer neural networks, in the regime where the size of the layers is commensurate with the number of samples in the training data. We show that…

In this paper, we gain the new almost unbiased Liu-type estimators to literature for the Bell regression model. We provide the superiority of the proposed estimator to its competitors such as the maximum likelihood estimator and Liu-type…

This work extends causal inference with stochastic confounders. We propose a new approach to variational estimation for causal inference based on a representer theorem with a random input space. We estimate causal effects involving latent…

Many econometrics textbooks imply that under mean independence of the regressors and the error term, the OLS parameters have a causal interpretation. We show that even when this assumption is satisfied, OLS might identify a pseudo-parameter…

Motivated by questions about dense (non-sparse) signals in high-dimensional data analysis, we study the unconditional out-of-sample prediction error (predictive risk) associated with three popular linear estimators for high-dimensional…

In a general linear model, this paper derives a necessary and sufficient condition under which two general ridge estimators coincide with each other. The condition is given as a structure of the dispersion matrix of the error term. Since…

It is well-known that, in Gaussian two-group separation, the optimally discriminating projection direction can be estimated without any knowledge on the group labels. In this work, we \revision{gather} several such unsupervised estimators…

Regression adjustment is broadly applied in randomized trials under the premise that it usually improves the precision of a treatment effect estimator. However, previous work has shown that this is not always true. To further understand…

Robins et al. (2008, 2017) applied the theory of higher order influence functions (HOIFs) to derive an estimator of the mean $\psi$ of an outcome Y in a missing data model with Y missing at random conditional on a vector X of continuous…

Stein unbiased risk estimation is generalized twice, from the Gaussian shift model to nonparametric families of smooth densities, and from the quadratic risk to more general divergence type distances. The development relies on a connection…