Related papers: Estimation of the $l_2$-norm and testing in sparse…
We consider least squares estimation in a general nonparametric regression model. The rate of convergence of the least squares estimator (LSE) for the unknown regression function is well studied when the errors are sub-Gaussian. We find…
Biased sampling and missing data complicates statistical problems ranging from causal inference to reinforcement learning. We often correct for biased sampling of summary statistics with matching methods and importance weighting. In this…
For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised…
We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…
We study the rate of decay of the probability of error for distinguishing between a sparse signal with noise, modeled as a sparse mixture, from pure noise. This problem has many applications in signal processing, evolutionary biology,…
This paper is concerned with estimation and inference for ultrahigh dimensional partially linear single-index models. The presence of high dimensional nuisance parameter and nuisance unknown function makes the estimation and inference…
The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the…
Consider the communication-constrained problem of nonparametric function estimation, in which each distributed terminal holds multiple i.i.d. samples. Under certain regularity assumptions, we characterize the minimax optimal rates for all…
In recent years, there has been a significant growth in research focusing on minimum $\ell_2$ norm (ridgeless) interpolation least squares estimators. However, the majority of these analyses have been limited to an unrealistic regression…
We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. The unknown error distribution is endowed with a symmetrized Dirichlet process mixture of Gaussians. For the…
One of the crucial tasks in many inference problems is the extraction of sparse information out of a given number of high-dimensional measurements. In machine learning, this is frequently achieved using, as a penality term, the $L_p$ norm…
This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…
A new variant of the Compressed Sensing problem is investigated when the number of measurements corrupted by errors is upper bounded by some value l but there are no more restrictions on errors. We prove that in this case it is enough to…
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…
The multivariate linear regression model with shuffled data and additive Gaussian noise arises in various correspondence estimation and matching problems. Focusing on the denoising aspect of this problem, we provide a characterization the…
In this paper we develop rate--optimal estimation procedures in the problem of estimating the $L_p$--norm, $p\in (0, \infty)$ of a probability density from independent observations. The density is assumed to be defined on $R^d$, $d\geq 1$…
A method for estimating nonlinear regression errors and their distributions without performing regression is presented. Assuming continuity of the modeling function the variance is given in terms of conditional probabilities extracted from…
We give a comprehensive theoretical characterization of a nonparametric estimator for the $L_2^2$ divergence between two continuous distributions. We first bound the rate of convergence of our estimator, showing that it is…
We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…
We study the estimation of $\beta$ for the nonlinear model $y = f(X\sp{\top}\beta) + \epsilon$ when $f$ is a nonlinear transformation that is known, $\beta$ has sparse nonzero coordinates, and the number of observations can be much smaller…