相关论文: Optimal Shrinkage of Eigenvalues in the Spiked Cov…

We consider sample covariance matrices $S_N=\frac{1}{p}\Sigma_N^{1/2}X_NX_N^* \Sigma_N^{1/2}$ where $X_N$ is a $N \times p$ real or complex matrix with i.i.d. entries with finite $12^{\rm th}$ moment and $\Sigma_N$ is a $N \times N$…

For a generalization of Johnstone's spiked model, a covariance matrix with eigenvalues all one but $M$ of them, the number of features $N$ comparable to the number of samples $n: N=N(n), M=M(n), \gamma^{-1} \leq \frac{N}{n} \leq \gamma$…

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…

We consider the problem of approximating the set of eigenvalues of the covariance matrix of a multivariate distribution (equivalently, the problem of approximating the "population spectrum"), given access to samples drawn from the…

We study the estimation of a high dimensional approximate factor model in the presence of both cross sectional dependence and heteroskedasticity. The classical method of principal components analysis (PCA) does not efficiently estimate the…

We consider the problem of estimating the principal components of a population correlation matrix from a limited number of measurement data. Using a combination of random matrix and information-theoretic tools, we show that all the…

Fund models are statistical descriptions of markets where all asset returns are spanned by the returns of a lower-dimensional collection of funds, modulo orthogonal noise. Equivalently, they may be characterised as models where the global…

This paper deals with a general class of transformation models that contains many important semiparametric regression models as special cases. It develops a self-induced smoothing for the maximum rank correlation estimator, resulting in…

We consider supervised learning problems in which set predictions provide explicit uncertainty estimates. Using Choquet integrals (a.k.a. Lov{\'a}sz extensions), we propose a convex loss function for nondecreasing subset-valued functions…

Optimal statistical decisions should transcend the language used to describe them. Yet, how do we guarantee that the choice of coordinates - the parameterisation of an optimisation problem - does not subtly dictate the solution? This paper…

Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…

The tools of optimal estimation are applied to the study of subgrid models for Large-Eddy Simulation of turbulence. The concept of optimal estimator is introduced and its properties are analyzed in the context of applications to a priori…

Stochastic processes are often used to model complex scientific problems in fields ranging from biology and finance to engineering and physical science. This paper investigates rate-optimal estimation of the volatility matrix of a…

Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…

The paper considers functional linear regression, where scalar responses $Y_1,...,Y_n$ are modeled in dependence of random functions $X_1,...,X_n$. We propose a smoothing splines estimator for the functional slope parameter based on a…

Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly…

Estimation of covariance matrices or their inverses plays a central role in many statistical methods. For these methods to work reliably, estimated matrices must not only be invertible but also well-conditioned. In this paper we present an…

We consider recovery of low-rank matrices from noisy data by shrinkage of singular values, in which a single, univariate nonlinearity is applied to each of the empirical singular values. We adopt an asymptotic framework, in which the matrix…

This review traces the evolution of theory that started when Charles Stein in 1955 [In Proc. 3rd Berkeley Sympos. Math. Statist. Probab. I (1956) 197--206, Univ. California Press] showed that using each separate sample mean from $k\ge3$…

High-dimensional covariance estimation is notoriously sensitive to outliers. While statistically optimal estimators exist for general heavy-tailed distributions, they often rely on computationally expensive techniques like semidefinite…