Related papers: Improved Covariance Matrix Estimator using Shrinka…
This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…
This paper examines the applicability of Random Matrix Theory to portfolio management in finance. Starting from a group of normally distributed stochastic processes with given correlations we devise an algorithm for removing noise from the…
Covariance matrix estimation is an important problem in multivariate data analysis, both from theoretical as well as applied points of view. Many simple and popular covariance matrix estimators are known to be severely affected by model…
In modern statistics, interests shift from pursuing the uniformly minimum variance unbiased estimator to reducing mean squared error (MSE) or residual squared error. Shrinkage based estimation and regression methods offer better prediction…
Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This…
Multivariate analysis of fMRI data has benefited substantially from advances in machine learning. Most recently, a range of probabilistic latent variable models applied to fMRI data have been successful in a variety of tasks, including…
Support vector machine (SVM) is one of the most popular classification algorithms in the machine learning literature. We demonstrate that SVM can be used to balance covariates and estimate average causal effects under the unconfoundedness…
The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…
The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of…
Variance components estimation and mixed model analysis are central themes in statistics with applications in numerous scientific disciplines. Despite the best efforts of generations of statisticians and numerical analysts, maximum…
A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In…
Estimating the disturbance or clutter covariance is a centrally important problem in radar space time adaptive processing (STAP). The disturbance covariance matrix should be inferred from training sample observations in practice. Large…
Covariate adjustment aims to improve the statistical efficiency of randomized trials by incorporating information from baseline covariates. Popular methods for covariate adjustment include analysis of covariance for continuous endpoints and…
Stacking regressions is an ensemble technique that forms linear combinations of different regression estimators to enhance predictive accuracy. The conventional approach uses cross-validation data to generate predictions from the…
Compositional data arise in many areas of research in the natural and biomedical sciences. One prominent example is in the study of the human gut microbiome, where one can measure the relative abundance of many distinct microorganisms in a…
Processing high-volume, streaming data is increasingly common in modern statistics and machine learning, where batch-mode algorithms are often impractical because they require repeated passes over the full dataset. This has motivated…
Selecting the optimal Markowitz porfolio depends on estimating the covariance matrix of the returns of $N$ assets from $T$ periods of historical data. Problematically, $N$ is typically of the same order as $T$, which makes the sample…
This paper provides some extended results on estimating parameter matrix of several regression models when the covariate or response possesses weaker moment condition. We study the $M$-estimator of Fan et al. (Ann Stat 49(3):1239--1266,…
In cryo-electron microscopy, the 3D electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy 2D images. The volume maps representing these potentials typically exhibit a great deal of…
This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman divergence losses. A major focus is on the derivation of a rate sharp minimax…