Related papers: Asymptotics of estimators for structured covarianc…
In this paper, we investigate the asymptotic behaviors of the extreme eigenvectors in a general spiked covariance matrix, where the dimension and sample size increase proportionally. We eliminate the restrictive assumption of the block…
General depth weighted scatter estimators are introduced and investigated. For general depth functions, we find out that these affine equivariant scatter estimators are Fisher consistent and unbiased for a wide range of multivariate…
This paper provides some useful tests for fitting a parametric single-index regression model when covariates are measured with error and validation data is available. We propose two tests whose consistency rates do not depend on the…
Latent factor models are widely used to measure unobserved latent traits in social and behavioral sciences, including psychology, education, and marketing. When used in a confirmatory manner, design information is incorporated, yielding…
We consider a multivariate linear response regression in which the number of responses and predictors is large and comparable with the number of observations, and the rank of the matrix of regression coefficients is assumed to be small. We…
Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn…
Randomized experiments are the gold standard for investigating causal relationships, with comparisons of potential outcomes under different treatment groups used to estimate treatment effects. However, outcomes with heavy-tailed…
We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data,…
In many applications of network analysis, it is important to distinguish between observed and unobserved factors affecting network structure. To this end, we develop spectral estimators for both unobserved blocks and the effect of…
Linear regression models depend directly on the design matrix and its properties. Techniques that efficiently estimate model coefficients by partitioning rows of the design matrix are increasingly popular for large-scale problems because…
We study sample covariance matrices arising from rectangular random matrices with i.i.d. columns. It was previously known that the resolvent of these matrices admits a deterministic equivalent when the spectral parameter stays bounded away…
Motivated by a neuroscience application we study the problem of statistical estimation of a high-dimensional covariance matrix with a block structure. The block model embeds a structural assumption: the population of items (neurons) can be…
Classical regression analysis relates the expectation of a response variable to a linear combination of explanatory variables. In this article, we propose a covariance regression model that parameterizes the covariance matrix of a…
In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…
We derive explicit expressions for a family of radially symmetric, non-differentiable, Spartan covariance functions in $\mathbb{R}^2$ that involve the modified Bessel function of the second kind. In addition to the characteristic length and…
We provide a unified analysis of the predictive risk of ridge regression and regularized discriminant analysis in a dense random effects model. We work in a high-dimensional asymptotic regime where $p, n \to \infty$ and $p/n \to \gamma \in…
We study the implicit regularization effects induced by (observation) weighting of pretrained features. For weight and feature matrices of bounded operator norms that are infinitesimally free with respect to (normalized) trace functionals,…
This article provides a central limit theorem for a consistent estimator of population eigenvalues with large multiplicities based on sample covariance matrices. The focus is on limited sample size situations, whereby the number of…
The complexity of semiparametric models poses new challenges to statistical inference and model selection that frequently arise from real applications. In this work, we propose new estimation and variable selection procedures for the…
We study the asymptotic behavior of the spectra of matrices of the form $S_n = \frac{1}{n}XX^*$ where $X =\sum_{r=1}^K X_r$, where $X_r = A_r^\frac{1}{2}Z_rB_r^\frac{1}{2}$, $K \in \mathbb{N}$ and $A_r,B_r$ are sequences of positive…