Related papers: Improved Covariance Matrix Estimator using Shrinka…
The accurate estimation of the noise covariance matrix (NCM) in a dynamic system is critical for state estimation and control, as it has a major influence in their optimality. Although a large number of NCM estimation methods have been…
We study estimation of the covariance matrix under relative condition number loss $\kappa(\Sigma^{-1/2} \hat{\Sigma} \Sigma^{-1/2})$, where $\kappa(\Delta)$ is the condition number of matrix $\Delta$, and $\hat{\Sigma}$ and $\Sigma$ are the…
This paper addresses the problem of inverse covariance (also known as precision matrix) estimation in high-dimensional settings. Specifically, we focus on two classes of estimators: linear shrinkage estimators with a target proportional to…
Recent studies stressed the fact that covariance matrices computed from empirical financial time series appear to contain a high amount of noise. This makes the classical Markowitz Mean-Variance Optimization model unable to correctly…
In this paper, we consider the spectrum sensing in cognitive radio networks when the impulsive noise appears. We propose a class of blind and robust detectors using M-estimators in eigenvalue based spectrum sensing method. The conventional…
Covariance matrix estimation is one of the most important problems in statistics. To accommodate the complexity of modern datasets, it is desired to have estimation procedures that not only can incorporate the structural assumptions of…
We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…
Estimation of the covariance matrix of asset returns from high frequency data is complicated by asynchronous returns, market mi- crostructure noise and jumps. One technique for addressing both asynchronous returns and market microstructure…
Estimating the clutter-plus-noise covariance matrix in high-dimensional STAP is challenging in the presence of Internal Clutter Motion (ICM) and a high noise floor. The problem becomes more difficult in low-sample regimes, where the Sample…
Covariance matrix estimation, a classical statistical topic, poses significant challenges when the sample size is comparable to or smaller than the number of features. In this paper, we frame covariance matrix estimation as a compound…
We derive an optimal shrinkage sample covariance matrix (SCM) estimator which is suitable for high dimensional problems and when sampling from an unspecified elliptically symmetric distribution. Specifically, we derive the optimal (oracle)…
In this paper, we propose the application of shrinkage strategies to estimate coefficients in the Bell regression models when prior information about the coefficients is available. The Bell regression models are well-suited for modeling…
We propose a data-driven way to reduce the noise of covariance matrices of nonstationary systems. In the case of stationary systems, asymptotic approaches were proved to converge to the optimal solutions. Such methods produce eigenvalues…
Randomization, as a key technique in clinical trials, can eliminate sources of bias and produce comparable treatment groups. In randomized experiments, the treatment effect is a parameter of general interest. Researchers have explored the…
The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state…
This work aims to deal with the optimal allocation instability problem of Markowitz's modern portfolio theory in high dimensionality. We propose a combined strategy that considers covariance matrix estimators from Random Matrix Theory~(RMT)…
Subsampling is a widely used and effective approach for addressing the computational challenges posed by massive datasets. Substantial progress has been made in developing non-uniform, probability-based subsampling schemes that prioritize…
We consider the problem of learning error covariance matrices for robotic state estimation. The convergence of a state estimator to the correct belief over the robot state is dependent on the proper tuning of noise models. During inference,…
Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection…
Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…