Related papers: A shrinkage estimation for large dimensional preci…

GraphSPME is an open source Python, R and C++ header-only package implement-ing non-parametric sparse precision matrix estimation along with asymptotic Stein-type shrinkage estimation of the covariance matrix. The user defines a potential…

In this paper we construct a shrinkage estimator of the global minimum variance (GMV) portfolio by a combination of two techniques: Tikhonov regularization and direct shrinkage of portfolio weights. More specifically, we employ a double…

Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…

In a coherent reliability system composed of multiple components configured according to a specific structure function, the distribution of system time to failure, or system lifetime, is often of primary interest. Accurate estimation of…

We study the denoising of low-rank matrices by singular value shrinkage. Recent work of Gavish and Donoho constructs a framework for finding optimal singular value shrinkers for a wide class of loss functions. We use this framework to…

We study the estimation of the high-dimensional covariance matrix andits eigenvalues under dynamic volatility models. Data under such modelshave nonlinear dependency both cross-sectionally and temporally. We firstinvestigate the empirical…

This paper develops a new statistical inference theory for the precision matrix of high-frequency data in a high-dimensional setting. The focus is not only on point estimation but also on interval estimation and hypothesis testing for…

Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…

We introduce a general framework for estimation of inverse covariance, or precision, matrices from heterogeneous populations. The proposed framework uses a Laplacian shrinkage penalty to encourage similarity among estimates from disparate,…

We study the consistency of sample mean-variance portfolios of arbitrarily high dimension that are based on Bayesian or shrinkage estimation of the input parameters as well as weighted sampling. In an asymptotic setting where the number of…

Marginal association summary statistics have attracted great attention in statistical genetics, mainly because the primary results of most genome-wide association studies (GWAS) are produced by marginal screening. In this paper, we study…

We analyze convergence rates of stochastic optimization procedures for non-smooth convex optimization problems. By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates of stochastic…

Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…

To tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling…

General ridge estimators are typical linear estimators in a general linear model. The class of them includes some shrinkage estimators in addition to classical linear unbiased estimators such as the ordinary least squares estimator and the…

Covariance estimation for matrix-valued data has received an increasing interest in applications. Unlike previous works that rely heavily on matrix normal distribution assumption and the requirement of fixed matrix size, we propose a class…

We propose new model selection criteria based on generalized ridge estimators dominating the maximum likelihood estimator under the squared risk and the Kullback-Leibler risk in multivariate linear regression. Our model selection criteria…

Inexpensive surrogates are useful for reducing the cost of science and engineering studies involving large-scale, complex computational models with many input parameters. A ridge approximation is one class of surrogate that models a…

We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…

This paper reviews advances in Stein-type shrinkage estimation for spherically symmetric distributions. Some emphasis is placed on developing intuition as to why shrinkage should work in location problems whether the underlying population…