Related papers: Optimal Shrinkage Estimator for High-Dimensional M…
Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the…
This manuscript presents an approach to perform generalized linear regression with multiple high dimensional covariance matrices as the outcome. Model parameters are proposed to be estimated by maximizing a pseudo-likelihood. When the data…
Stein showed that the multivariate sample mean is outperformed by "shrinking" to a constant target vector. Ledoit and Wolf extended this approach to the sample covariance matrix and proposed a multiple of the identity as shrinkage target.…
Shrinkage methods are frequently used to improve the precision of least squares estimators of fixed effects. However, widely used shrinkage estimators guarantee improved precision only under strong distributional assumptions. I develop an…
This work addresses large dimensional covariance matrix estimation with unknown mean. The empirical covariance estimator fails when dimension and number of samples are proportional and tend to infinity, settings known as Kolmogorov…
The estimation of the mean matrix of the multivariate normal distribution is addressed in the high dimensional setting. Efron-Morris-type linear shrinkage estimators based on ridge estimators for the precision matrix instead of the…
We study shrinkage estimation of the mean parameters of a class of multivariate distributions for which the diagonal entries of the corresponding covariance matrix are certain quadratic functions of the mean parameter. This class of…
We propose a new pivotal method for estimating high-dimensional matrices. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix $A\_0$ corrupted by noise. We propose a new method for estimating…
The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…
In large-scale, data-driven applications, parameters are often only known approximately due to noise and limited data samples. In this paper, we focus on high-dimensional optimization problems with linear constraints under uncertain…
The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…
A highly popular regularized (shrinkage) covariance matrix estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward the grand mean of the eigenvalues…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
Consider estimating the n by p matrix of means of an n by p matrix of independent normally distributed observations with constant variance, where the performance of an estimator is judged using a p by p matrix quadratic error loss function.…
We propose a new sufficient dimension reduction approach designed deliberately for high-dimensional classification. This novel method is named maximal mean variance (MMV), inspired by the mean variance index first proposed by Cui, Li and…
In many astrophysical settings covariance matrices of large datasets have to be determined empirically from a finite number of mock realisations. The resulting noise degrades inference and precludes it completely if there are fewer…
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…
This paper offers a new approach to address the model uncertainty in (potentially) divergent-dimensional single-index models (SIMs). We propose a model-averaging estimator based on cross-validation, which allows the dimension of covariates…
The Support Vector Machine (SVM) is one of the most widely used classification methods. In this paper, we consider the soft-margin SVM used on data points with independent features, where the sample size $n$ and the feature dimension $p$…