Related papers: SCOPE: Spectral Concentration by Distributionally …
This paper presents a novel approach to constructing estimators that dominate the classical James-Stein estimator under the quadratic loss for multivariate normal means. Building on Stein's risk representation, we introduce a new sufficient…
Consider an $n \times p$ data matrix $X$ whose rows are independently sampled from a population with covariance $\Sigma$. When $n,p$ are both large, the eigenvalues of the sample covariance matrix are substantially different from those of…
This paper presents Sparse Gradient Descent as a solution for variable selection in convex piecewise linear regression, where the model is given as the maximum of $k$-affine functions $ x \mapsto \max_{j \in [k]} \langle a_j^\star, x…
We investigate the bias and error in estimates of the cosmological parameter covariance matrix, due to sampling or modelling the data covariance matrix, for likelihood width and peak scatter estimators. We show that these estimators do not…
We introduce and analyse a new nonparametric estimator of a multi-dimensional density. Our smooth projection estimator (SPE) is defined by a least squares projection of the sample onto an infinite dimensional mixture class via an…
We consider the problem of precision matrix estimation where, due to extraneous confounding of the underlying precision matrix, the data are independent but not identically distributed. While such confounding occurs in many scientific…
In this paper we estimate the mean-variance portfolio in the high-dimensional case using the recent results from the theory of random matrices. We construct a linear shrinkage estimator which is distribution-free and is optimal in the sense…
We consider the problem of estimating the mean vector $\theta$ of a $d$-dimensional spherically symmetric distributed $X$ based on balanced loss functions of the forms: {\bf (i)} $\omega \rho(\|\de-\de_{0}\|^{2}) +(1-\omega)\rho(\|\de -…
A new wave of work on covariance cleaning and nonlinear shrinkage has delivered asymptotically optimal analytical solutions for large covariance matrices. The same framework has been generalized to empirical cross-covariance matrices, whose…
In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and…
We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…
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…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
Managing insurance and financial risk when data is limited is a key task in the insurance industry. In this paper, we focus on cases where the risk distribution is modeled as a mixture with some components estimable to high precision or…
The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…
Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization…
Mean-variance portfolio decisions that combine prediction and optimisation have been shown to have poor empirical performance. Here, we consider the performance of various shrinkage methods by their efficient frontiers under different…
Due to the complexity of order statistics, the finite sample behaviour of robust statistics is generally not analytically solvable. While the Monte Carlo method can provide approximate solutions, its convergence rate is typically very slow,…
Distributed aggregation allows the derivation of a given global aggregate property from many individual local values in nodes of an interconnected network system. Simple aggregates such as minima/maxima, counts, sums and averages have been…
In this paper we propose an estimator of spot covariance matrix which ensure symmetric positive semi-definite estimations. The proposed estimator relies on a suitable modification of the Fourier covariance estimator in Malliavin and Mancino…