A New Parameter-Free Two-Bit Covariance Estimator with Improved Operator Norm Error Rate for Sub-Gaussian Distributions
This paper introduces a novel, parameter-free, two-bit covariance estimator for sub-Gaussian distributions that achieves a near-optimal operator norm error rate, improving upon existing methods, particularly when the covariance matrix's diagonal is dominated by a few large entries.
A New Structured Estimator for Large Covariance Matrices Using Pairwise and Spatial Covariates: Applied to Total Fertility Rate Data
This paper introduces a novel structured covariance estimator (SCE) for high-dimensional data with limited observations, leveraging pairwise and spatial covariates to enhance estimation accuracy, particularly in scenarios like modeling the total fertility rate across numerous countries.
Covariance Estimation Using Markov Chain Monte Carlo: Reducing Query Complexity for Dependent Samples
Markov chain Monte Carlo (MCMC) methods can significantly reduce the query complexity of covariance estimation for distributions satisfying a Poincaré inequality, compared to estimators using independent samples.
The Quadratic Optimization Bias of Large Covariance Matrices in High Dimension and Low Sample Size Settings
Estimating covariance matrices in high-dimensional settings poses significant challenges for quadratic optimization problems, as traditional methods like Principal Component Analysis (PCA) can lead to substantial discrepancies between estimated and realized optima. This paper introduces a novel method for correcting the bias in sample eigenvectors, leading to improved covariance estimation and more accurate solutions for quadratic optimization tasks.
Ridge-Regularized Covariance Graphical Lasso for High Dimensional Data
This paper proposes a novel method for estimating sparse covariance matrices in high-dimensional settings, unifying existing approaches like MLE, L1-penalized log-likelihood optimization, and ridge regularization into a single framework called ridge-regularized covglasso.
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