Related papers: Estimation under matrix quadratic loss and matrix …
We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the…
This paper proposes an estimation framework to assess the performance of sorting over perturbed/noisy data. In particular, the recovering accuracy is measured in terms of Minimum Mean Square Error (MMSE) between the values of the sorting…
An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of…
Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
This paper introduces a subspace method for the estimation of an array covariance matrix. It is shown that when the received signals are uncorrelated, the true array covariance matrices lie in a specific subspace whose dimension is…
In this paper, a shrinkage estimator for the population mean is proposed under known quadratic loss functions with unknown covariance matrices. The new estimator is non-parametric in the sense that it does not assume a specific parametric…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…
The problem of structured matrix estimation has been studied mostly under strong noise dependence assumptions. This paper considers a general framework of noisy low-rank-plus-sparse matrix recovery, where the noise matrix may come from any…
We consider Bayesian inference of signals with vector-valued entries. Extending concentration techniques from the mathematical physics of spin glasses, we show that the matrix-valued minimum mean-square error concentrates when the size of…
Low-rank matrix estimation plays a central role in various applications across science and engineering. Recently, nonconvex formulations based on matrix factorization are provably solved by simple gradient descent algorithms with strong…
This paper considers the estimation of Shannon entropy for discrete distributions with countably infinite support. While minimax rates for finite-support distributions are established, infinite-support distributions present distinct…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
We explore how violations of the often-overlooked standard assumption that the random effects model matrix in a linear mixed model is fixed (and thus independent of the random effects vector) can lead to bias in estimators of estimable…
This paper presents an integrated framework for estimation and inference from generalized linear models using adjusted score equations that result in mean and median bias reduction. The framework unifies theoretical and methodological…
We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by…
The Bayes linear estimator is derived by minimizing the Bayes risk with respect to the squared loss function. Non-unbiased estimators such as ordinary ridge, typical shrinkage, fractional rank, and restricted least squares estimators, as…
This paper continues the authors' previous study (SIAM J. Math. Anal., 2016) of the trend toward equilibrium of the Becker-D\"oring equations with subcritical mass, by characterizing certain fine properties of solutions to the linearized…
We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis…
We consider robust low rank matrix estimation as a trace regression when outputs are contaminated by adversaries. The adversaries are allowed to add arbitrary values to arbitrary outputs. Such values can depend on any samples. We deal with…