Related papers: A Bilateral Bound on the Mean-Square Error for Est…
Designs which are minimax in the presence of model misspecifications have been constructed so as to minimize the maximum, over classes of alternate response models, of the integrated mean squared error of the predicted values. This mean…
In Bayesian statistics, the marginal likelihood is used for model selection and averaging, yet it is often challenging to compute accurately for complex models. Approaches such as bridge sampling, while effective, may suffer from issues of…
We consider the problem of estimating the error variance in a general linear model when the error distribution is assumed to be spherically symmetric, but not necessary Gaussian. In particular we study the case of a scale mixture of…
This paper studies the minimum mean squared error (MMSE) of estimating $\mathbf{X} \in \mathbb{R}^d$ from the noisy observation $\mathbf{Y} \in \mathbb{R}^k$, under the assumption that the noise (i.e., $\mathbf{Y}|\mathbf{X}$) is a member…
We present a proposal to deal with the non-normality issue in the context of regression models with measurement errors when both the response and the explanatory variable are observed with error. We extend the normal model by jointly…
This paper develops a bias correction scheme for a multivariate normal model under a general parameterization. In the model, the mean vector and the covariance matrix share the same parameters. It includes many important regression models…
Measurement error occurs when a covariate influencing a response variable is corrupted by noise. This can lead to misleading inference outcomes, particularly in problems where accurately estimating the relationship between covariates and…
The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…
The multivariate errors-in-variables regression model is applicable when both dependent and independent variables in a multivariate regression are subject to measurement errors. In such a scenario it is long established that the traditional…
Diffusion bridge models have recently become a powerful tool in the field of generative modeling. In this work, we leverage their power to address another important problem in machine learning and information theory, the estimation of the…
We propose the use of a simple intuitive principle for measuring algorithmic classification bias: the significance of the differences in a classifier's error rates across the various demographics is inversely commensurate with the sample…
Threshold and ambiguity phenomena are studied in Part 1 of this work where approximations for the mean-squared-error (MSE) of the maximum likelihood estimator are proposed using the method of interval estimation (MIE), and where approximate…
We analyze the mean-squared error (MSE) performance of widely linear (WL) and conventional subspace-based channel estimation for single-input multiple-output (SIMO) flat-fading channels employing binary phase-shift-keying (BPSK) modulation…
Current PAC-Bayes generalisation bounds are restricted to scalar metrics of performance, such as the loss or error rate. However, one ideally wants more information-rich certificates that control the entire distribution of possible…
We present novel lower bounds on the mean square error (MSE) of the location estimation of an emitting source via a network where the sensors are deployed randomly. The sensor locations are modeled as a homogenous Poisson point process. In…
We generalize the na\"ive estimator of a Poisson regression model with measurement errors as discussed in Kukush et al. [1]. The explanatory variable is not always normally distributed as they assume. In this study, we assume that the…
Ideally, a meta-analysis will summarize data from several unbiased studies. Here we consider the less than ideal situation in which contributing studies may be compromised by measurement error. Measurement error affects every study design,…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
This paper proposes a class of ratio type estimators of finite population variance, when the population variance of an auxiliary character is known. Asymptotic expression for mean square error (MSE) is derived and compared with the mean…
The minimum mean-square error (MMSE) achievable by optimal estimation of a random variable $Y\in\mathbb{R}$ given another random variable $X\in\mathbb{R}^{d}$ is of much interest in a variety of statistical settings. In the context of…