Related papers: A Lower Bound on the Estimator Variance for the Sp…

We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function $f$ is observed with additive Gaussian white noise. The function $f$ is assumed to have…

We propose an estimator for the singular vectors of high-dimensional low-rank matrices corrupted by additive subgaussian noise, where the noise matrix is allowed to have dependence within rows and heteroskedasticity between them. We prove…

In this paper, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions of a common variable such as time. We consider the case that the response and the predictor…

We study parameter estimation and asymptotic inference for sparse nonlinear regression. More specifically, we assume the data are given by $y = f( x^\top \beta^* ) + \epsilon$, where $f$ is nonlinear. To recover $\beta^*$, we propose an…

We consider reduced-rank modeling of the white noise covariance matrix in a large dimensional vector autoregressive (VAR) model. We first propose the reduced-rank covariance estimator under the setting where independent observations are…

Variational inference is a powerful tool for approximate inference. However, it mainly focuses on the evidence lower bound as variational objective and the development of other measures for variational inference is a promising area of…

Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…

Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

Drawing statistical inferences from large datasets in a model-robust way is an important problem in statistics and data science. In this paper, we propose methods that are robust to large and unequal noise in different observational units…

This paper addresses the estimation of signals with sublinear sparsity sent over the additive white Gaussian noise channel. This fundamental problem arises in designing denoisers used in message-passing algorithms for sublinear sparsity.…

We investigate a problem estimating coefficients of linear regression under sparsity assumption when covariates and noises are sampled from heavy tailed distributions. Additionally, we consider the situation where not only covariates and…

This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this…

In this manuscript, we study quantile regression in partial functional linear model where response is scalar and predictors include both scalars and multiple functions. Wavelet basis are adopted to better approximate functional slopes while…

We consider the nonparametric estimation problem of time-dependent multivariate functions observed in a presence of additive cylindrical Gaussian white noise of a small intensity. We derive minimax lower bounds for the $L^2$-risk in the…

The high-dimensional linear model $y = X \beta^0 + \epsilon$ is considered and the focus is put on the problem of recovering the support $S^0$ of the sparse vector $\beta^0.$ We introduce Lasso-Zero, a new $\ell_1$-based estimator whose…

This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…

Gaussian Processes (GP) have become popular machine-learning methods for kernel-based learning on datasets with complicated covariance structures. In this paper, we present a novel extension to the GP framework using a contaminated normal…

A parameter estimation problem is considered for a linear stochastic hyperbolic equation driven by additive space-time Gaussian white noise. The damping/amplification operator is allowed to be unbounded. The estimator is of spectral type…

We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and…