Related papers: Multivariate Analysis of Nonparametric Estimates o…
In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…
This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified.…
A new nonparametric estimator for Toeplitz covariance matrices is proposed. This estimator is based on a data transformation that translates the problem of Toeplitz covariance matrix estimation to the problem of mean estimation in an…
We consider estimation of a sparse parameter vector that determines the covariance matrix of a Gaussian random vector via a sparse expansion into known "basis matrices". Using the theory of reproducing kernel Hilbert spaces, we derive lower…
When nonlinear measures are estimated from sampled temporal signals with finite-length, a radius parameter must be carefully selected to avoid a poor estimation. These measures are generally derived from the correlation integral which…
The current paper presents a novel machinery for studying non-asymptotic minimax estimation of high-dimensional matrices, which yields tight minimax rates for a large collection of loss functions in a variety of problems. Based on the…
We present algorithms for nonparametric regression in settings where the data are obtained sequentially. While traditional estimators select bandwidths that depend upon the sample size, for sequential data the effective sample size is…
Distribution regression seeks to estimate the conditional distribution of a multivariate response given a continuous covariate. This approach offers a more complete characterization of dependence than traditional regression methods.…
A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…
There has been an increasing interest in testing the equality of large Pearson's correlation matrices. However, in many applications it is more important to test the equality of large rank-based correlation matrices since they are more…
The maximum correlation of functions of a pair of random variables is an important measure of stochastic dependence. It is known that this maximum nonlinear correlation is identical to the absolute value of the Pearson correlation for a…
We investigate simulation-based bandpower covariance matrices commonly used in cosmological parameter inferences such as the estimation of the tensor-to-scalar ratio $r$. We find that upper limits on $r$ can be biased low by tens of…
Mixed-effect models are widely used for the analysis of correlated data such as longitudinal data and repeated measures. In this article, we study an approach to the nonparametric estimation of mixed-effect models. We consider models with…
The sparse signal processing literature often uses random sensing matrices to obtain performance guarantees. Unfortunately, in the real world, sensing matrices do not always come from random processes. It is therefore desirable to evaluate…
We consider estimating the parametric components of semi-parametric multiple index models in a high-dimensional and non-Gaussian setting. Such models form a rich class of non-linear models with applications to signal processing, machine…
Interval-censoring frequently occurs in studies of chronic diseases where disease status is inferred from intermittently collected biomarkers. Although many methods have been developed to analyze such data, they typically assume perfect…
In this paper, we show that the diagonal of a high-dimensional sample covariance matrix stemming from $n$ independent observations of a $p$-dimensional time series with finite fourth moments can be approximated in spectral norm by the…
We give a non-asymptotic bound on the spectral norm of a $d\times d$ matrix $X$ with centered jointly Gaussian entries in terms of the covariance matrix of the entries. In some cases, this estimate is sharp and removes the $\sqrt{\log d}$…
The problem of estimating the covariance matrix $\Sigma$ of a $p$-variate distribution based on its $n$ observations arises in many data analysis contexts. While for $n>p$, the classical sample covariance matrix $\hat{\Sigma}_n$ is a good…
In high-dimensional linear regression, the goal pursued here is to estimate an unknown regression function using linear combinations of a suitable set of covariates. One of the key assumptions for the success of any statistical procedure in…