相关论文: Complex Mean and Variance of Linear Regression Mod…

The importance of exploring a potential integration among surveys has been acknowledged in order to enhance effectiveness and minimize expenses. In this work, we employ the alignment method to combine information from two different surveys…

This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…

Minimizing the Mean Squared Error (MSE) is a key objective in machine learning and is commonly used for imputing missing values. While this approach provides accurate point estimates, it introduces systematic biases in downstream analyses.…

A robust and sparse estimator for multinomial regression is proposed for high dimensional data. Robustness of the estimator is achieved by trimming the observations, and sparsity of the estimator is obtained by the elastic net penalty,…

We derive the bias, variance, covariance, and mean square error of the standard lag windowed correlogram estimator both with and without sample mean removal for complex white noise with an arbitrary mean. We find that the arbitrary mean…

Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…

In this paper, we study a new notion of scaled minimaxity for sparse estimation in high-dimensional linear regression model. We present more optimistic lower bounds than the one given by the classical minimax theory and hence improve on…

We obtain robust and computationally efficient estimators for learning several linear models that achieve statistically optimal convergence rate under minimal distributional assumptions. Concretely, we assume our data is drawn from a…

A new Lp-norm constraint least mean square (Lp-LMS) algorithm with new strategy of varying p is presented, which is applied to system identification in this letter. The parameter p is iteratively adjusted by the gradient method applied to…

This paper is centered around the approximation of dynamical systems by means of Gaussian processes. To this end, trajectories of such systems must be collected to be used as training data. The measurements of these trajectories are…

Errors in variables (Deming) regression of measurements spanning a wide range of values requires appropriate weighting to reflect nonconstant variance. Precision profile models, mathematical relationships between measurement variance and…

We prove a new and general concentration inequality for the excess risk in least-squares regression with random design and heteroscedastic noise. No specific structure is required on the model, except the existence of a suitable function…

The linear regression models are widely used statistical techniques in numerous practical applications. The standard regression model requires several assumptions about the regres- sors and the error term. The regression parameters are…

We present an adaptive smoother for linear state-space models with unknown process and measurement noise covariances. The proposed method utilizes the variational Bayes technique to perform approximate inference. The resulting smoother is…

For the lognormal distribution, an unbiased estimator of the squared coefficient of variation is derived from the relative ratio of sample arithmetic to harmonic means. Analytical proofs and simulation results are presented.

Standard noise radars, as well as noise-type radars such as quantum two-mode squeezing radar, are characterized by a covariance matrix with a very specific structure. This matrix has four independent parameters: the amplitude of the…

Robust methods, though ubiquitous in practice, are yet to be fully understood in the context of regularized estimation and high dimensions. Even simple questions become challenging very quickly. For example, classical statistical theory…

This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by…

We address the question of estimating Kullback-Leibler losses rather than squared losses in recovery problems where the noise is distributed within the exponential family. Inspired by Stein unbiased risk estimator (SURE), we exhibit…

This paper presents a practical and simple fully nonparametric multivariate smoothing procedure that adapts to the underlying smoothness of the true regression function. Our estimator is easily computed by successive application of existing…