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

A class of robust estimators of scatter applied to information-plus-impulsive noise samples is studied, where the sample information matrix is assumed of low rank; this generalizes the study of (Couillet et al., 2013b) to spiked random…

This paper proposes a statistically optimal approach for learning a function value using a confidence interval in a wide range of models, including general non-parametric estimation of an expected loss described as a stochastic programming…

We study the problem of high-dimensional covariance estimation under the constraint that the partial correlations are nonnegative. The sign constraints dramatically simplify estimation: the Gaussian maximum likelihood estimator is well…

We develop an adaptive monotone shrinkage estimator for regression models with the following characteristics: i) dense coefficients with small but important effects; ii) a priori ordering that indicates the probable predictive importance of…

We study risk of the minimum norm linear least squares estimator in when the number of parameters $d$ depends on $n$, and $\frac{d}{n} \rightarrow \infty$. We assume that data has an underlying low rank structure by restricting ourselves to…

We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…

The determination of the covariance matrix and its inverse, the precision matrix, is critical in the statistical analysis of cosmological measurements. The covariance matrix is typically estimated with a limited number of simulations at…

In a linear regression model with random design, we consider a family of candidate models from which we want to select a `good' model for prediction out-of-sample. We fit the models using block shrinkage estimators, and we focus on the…

The Metropolis-Hastings algorithm has been extensively studied in the estimation and simulation literature, with most prior work focusing on convergence behavior and asymptotic theory. However, its covariance structure-an important…

We develop and evaluate point and interval estimates for the random effects $\theta_i$, having made observations $y_i|\theta_i\stackrel{\m athit{ind}}{\sim}N[\theta_i,V_i],i=1,...,k$ that follow a two-level Normal hierarchical model.…

We consider general high-dimensional spiked sample covariance models and show that their leading sample spiked eigenvalues and their linear spectral statistics are asymptotically independent when the sample size and dimension are…

In recent years, sparse principal component analysis has emerged as an extremely popular dimension reduction technique for high-dimensional data. The theoretical challenge, in the simplest case, is to estimate the leading eigenvector of a…

Estimating covariance matrices is a problem of fundamental importance in multivariate statistics. In practice it is increasingly frequent to work with data matrices $X$ of dimension $n\times p$, where $p$ and $n$ are both large. Results…

In this paper, we prove that functional sliced inverse regression (FSIR) achieves the optimal (minimax) rate for estimating the central space in functional sufficient dimension reduction problems. First, we provide a concentration…

We consider in this paper the problem of optimal experiment design where a decision maker can choose which points to sample to obtain an estimate $\hat{\beta}$ of the hidden parameter $\beta^{\star}$ of an underlying linear model. The key…

In this paper we propose a dimension-reduction strategy in order to improve the performance of importance sampling in high dimension. The idea is to estimate variance terms in a small number of suitably chosen directions. We first prove…

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,…

Survey sampling is concerned with the estimation of finite population parameters. In practice, survey data suffer from item nonresponse, which is commonly handled through imputation, i.e., replacing missing values with predicted values. As…

Longitudinal biomedical studies monitor individuals over time to capture dynamics in brain development, disease progression, and treatment effects. However, estimating trajectories of brain biomarkers is challenging due to biological…

The problem of estimating sparse eigenvectors of a symmetric matrix attracts a lot of attention in many applications, especially those with high dimensional data set. While classical eigenvectors can be obtained as the solution of a…