English
Related papers

Related papers: Multi Anchor Point Shrinkage for the Sample Covari…

200 papers

Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…

Computational Physics · Physics 2021-08-24 Ziming Liu , Sitian Qian , Yixuan Wang , Yuxuan Yan , Tianyi Yang

We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed…

Machine Learning · Statistics 2015-03-19 Teng Zhang , Gilad Lerman

Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…

Statistics Theory · Mathematics 2017-10-30 Raphael Hauser , Raul Kangro , Jüri Lember , Heinrich Matzinger

This paper constructs improved estimators of the means in the Gaussian saturated one-way layout with an ordinal factor. The least squares estimator for the mean vector in this saturated model is usually inadmissible. The hybrid shrinkage…

Statistics Theory · Mathematics 2007-06-13 Rudolf Beran

The beta regression model is a useful framework to model response variables that are rates or proportions, that is to say, response variables which are continuous and restricted to the interval (0,1). As with any other regression model,…

Methodology · Statistics 2024-06-27 Luis Firinguetti , Manuel González-Navarrete , Romer Machaca-Aguilar

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…

Statistical Finance · Quantitative Finance 2024-07-08 Taras Bodnar , Nestor Parolya , Erik Thorsén

Statistical inference for sparse covariance matrices is crucial to reveal dependence structure of large multivariate data sets, but lacks scalable and theoretically supported Bayesian methods. In this paper, we propose beta-mixture…

Statistics Theory · Mathematics 2021-01-13 Kyoungjae Lee , Seongil Jo , Jaeyong Lee

To recover a low rank structure from a noisy matrix, truncated singular value decomposition has been extensively used and studied. Recent studies suggested that the signal can be better estimated by shrinking the singular values. We pursue…

Methodology · Statistics 2014-11-25 Julie Josse , Sylvain Sardy

Robust and reliable covariance estimates play a decisive role in financial and many other applications. An important class of estimators is based on Factor models. Here, we show by extensive Monte Carlo simulations that covariance matrices…

Portfolio Management · Quantitative Finance 2015-03-19 Daniel Bartz , Kerr Hatrick , Christian W. Hesse , Klaus-Robert Müller , Steven Lemm

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.…

Methodology · Statistics 2014-12-08 Daniel Bartz , Johannes Höhne , Klaus-Robert Müller

We address high dimensional covariance estimation for elliptical distributed samples, which are also known as spherically invariant random vectors (SIRV) or compound-Gaussian processes. Specifically we consider shrinkage methods that are…

Methodology · Statistics 2015-05-20 Yilun Chen , Ami Wiesel , Alfred O. Hero

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…

Statistics Theory · Mathematics 2013-05-27 Zongming Ma

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Data Structures and Algorithms · Computer Science 2021-06-07 Agniva Chowdhury , Petros Drineas , David P. Woodruff , Samson Zhou

We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by…

Statistics Theory · Mathematics 2016-11-21 Ashwini Maurya

Shrinkage for time-varying parameter (TVP) models is investigated within a Bayesian framework, with the aim to automatically reduce time-varying parameters to static ones, if the model is overfitting. This is achieved through placing the…

Methodology · Statistics 2018-06-05 Angela Bitto , Sylvia Frühwirth-Schnatter

Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…

Information Theory · Computer Science 2014-06-19 Andrea Montanari , Emile Richard

This paper introduces a neural network-based nonlinear shrinkage estimator of covariance matrices for the purpose of minimum variance portfolio optimization. It is a hybrid approach that integrates statistical estimation with machine…

Machine Learning · Computer Science 2026-01-23 Liusha Yang , Siqi Zhao , Shuqi Chai

In this work we consider the estimation of spatio-temporal covariance matrices in the low sample non-Gaussian regime. We impose covariance structure in the form of a sum of Kronecker products decomposition (Tsiligkaridis et al. 2013,…

Methodology · Statistics 2014-05-14 Kristjan Greenewald , Alfred O. Hero

Shrinkage estimators of covariance are an important tool in modern applied and theoretical statistics. They play a key role in regularized estimation problems, such as ridge regression (aka Tykhonov regularization), regularized discriminant…

Statistics Theory · Mathematics 2011-05-10 Noureddine El Karoui , Holger Koesters

Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…

Statistics Theory · Mathematics 2009-01-29 Iain M Johnstone , Arthur Yu Lu