Related papers: Complex Mean and Variance of Linear Regression Mod…

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…

We address numerical differentiation under coarse, non-uniform sampling and Gaussian noise. A maximum-likelihood estimator with $L_2$-norm constraint on a higher-order derivative is obtained, yielding spline-based solution. We introduce a…

This paper deals with the problem of estimating a slope parameter in a simple linear regression model, where independent variables have functional measurement errors. Measurement errors in independent variables, as is well known, cause…

For the sparse vector model, we consider estimation of the target vector, of its L2-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with…

Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…

In this paper we refine the procedure proposed by Lin et al. (2015) to estimate the density at a given quantile based on a resampling method. The approach consists on generating multiple samples of the zero-mean Gaussian variable from which…

Fine stratification is a popular design as it permits the stratification to be carried out to the fullest possible extent. Some examples include the Current Population Survey and National Crime Victimization Survey both conducted by the…

A low-complexity model for signal quality prediction in a nonlinear fiber-optical network is developed. The model, which builds on the Gaussian noise model, takes into account the signal degradation caused by a combination of chromatic…

In this paper, we study the problem of sparse mean estimation under adversarial corruptions, where the goal is to estimate the $k$-sparse mean of a heavy-tailed distribution from samples contaminated by adversarial noise. Existing methods…

To recover a low rank structure from a noisy matrix, truncated singular value decomposition has been extensively used and studied. Recent studies suggested that the signal can be better estimated by shrinking the singular values. We pursue…

This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…

Sparse linear regression methods such as Lasso require a tuning parameter that depends on the noise variance, which is typically unknown and difficult to estimate in practice. In the presence of heavy-tailed noise or adversarial outliers,…

We propose a procedure to handle the problem of Gaussian regression when the variance is unknown. We mix least-squares estimators from various models according to a procedure inspired by that of Leung and Barron (2007). We show that in some…

Variable selection for a multiple regression model (Noisy Linear Perceptron) is studied with a mean field approximation. In our Bayesian framework, variable selection is formulated as estimation of discrete parameters that indicate a subset…

We investigate a problem estimating coefficients of linear regression under sparsity assumption when covariates and noises are sampled from heavy tailed distributions. Additionally, we consider the situation where not only covariates and…

This paper presents a robust regression approach for image binarization under significant background variations and observation noises. The work is motivated by the need of identifying foreground regions in noisy microscopic image or…

The bias-compensated set-membership normalised LMS (BCSMNLMS) algorithm is proposed based on the concept of set-membership filtering, which incorporates the bias-compensation technique to mitigate the negative effect of noisy inputs.…

Recent algebraic parametric estimation techniques led to point-wise derivative estimates by using only the iterated integral of a noisy observation signal. In this paper, we extend such differentiation methods by providing a larger choice…

This paper introduces a new biased estimator for the negative binomial regression model that is a generalization of Liu-type estimator proposed for the linear model in [12]. Since the variance of the maximum likelihood estimator (MLE) is…

This paper considers estimation of a random variable in Poisson noise with signal scaling coefficient and dark current as explicit parameters of the noise model. Specifically, the paper focuses on properties of the conditional mean…