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An approximate mean square error (MSE) expression for the performance analysis of implicitly defined estimators of non-random parameters is proposed. An implicitly defined estimator (IDE) declares the minimizer/maximizer of a selected…
We study the least square estimator, in the framework of simple linear regression, when the deviance term $\varepsilon$ with respect to the linear model is modeled by a uniform distribution. In particular, we give the law of this estimator,…
In this paper, we consider the problem of recovering random graph signals with complex values. For general Bayesian estimation of complex-valued vectors, it is known that the widely-linear minimum mean-squared-error (WLMMSE) estimator can…
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…
State estimation is a classical problem in quantum information. In optimization of estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use…
We propose a rectangular rotational invariant estimator to recover a real matrix from noisy matrix observations coming from an arbitrary additive rotational invariant perturbation, in the large dimension limit. Using the Bayes-optimality of…
Traditional covariate selection methods for causal inference focus on achieving unbiasedness and asymptotic efficiency. In many practical scenarios, researchers must estimate causal effects from observational data with limited sample sizes…
In this note, we concentrate on the backward error of the equality constrained indefinite least squares problem. For the normwise backward error of the equality constrained indefinite least square problem, we adopt the linearization method…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
The Bayes linear estimator is derived by minimizing the Bayes risk with respect to the squared loss function. Non-unbiased estimators such as ordinary ridge, typical shrinkage, fractional rank, and restricted least squares estimators, as…
In order to function reliably, synthetic molecular circuits require mechanisms that allow them to adapt to environmental disturbances. Least mean squares (LMS) schemes, such as commonly encountered in signal processing and control, provide…
We propose an adversarial evaluation framework for sensitive feature inference based on minimum mean-squared error (MMSE) estimation with a finite sample size and linear predictive models. Our approach establishes theoretical lower bounds…
A novel estimation approach for a general class of semi-parametric multivariate time series models is introduced where the conditional mean is modeled through parametric functions. The focus of the estimation is the conditional mean…
The LMS algorithm is one of the most widely used techniques in adaptive filtering. Accurate modeling of the algorithm in various circumstances is paramount to achieving an efficient adaptive Wiener filter design process. In the recent…
The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov…
In the context of Independent Component Analysis (ICA), noisy mixtures pose a dilemma regarding the desired objective. On one hand, a "maximally separating" solution, providing the minimal attainable Interference-to-Source-Ratio (ISR),…
Most studies of adaptive algorithm behavior consider performance measures based on mean values such as the mean-square error. The derived models are useful for understanding the algorithm behavior under different environments and can be…
We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the…
This study focuses on addressing the challenge of solving the reduced biquaternion equality constrained least squares (RBLSE) problem. We develop algebraic techniques to derive real and complex solutions for the RBLSE problem by utilizing…
Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with…