Related papers: Estimation of the $l_2$-norm and testing in sparse…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
In this paper we propose a new test for the hypothesis of a constant coefficient of variation in the common nonparametric regression model. The test is based on an estimate of the $L^2$-distance between the square of the regression function…
A formal likelihood ratio hypothesis test for the validity of a parametric regression function is proposed, using a large-dimensional, nonparametric double cone alternative. For example, the test against a constant function uses the…
This article investigates the least squares estimators (LSE) for the unknown parameters in stochastic differential equations (SDEs) that are affected by L\'evy noise, particularly when the sample paths are sparse. Specifically, given $n$…
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 describe, in the detection of multi-sample aligned sparse signals, the critical boundary separating detectable from nondetectable signals, and construct tests that achieve optimal detectability: penalized versions of the Berk-Jones and…
The problem tackled in this paper is the determination of sample size for a given level and power in the context of a simple linear regression model. At a technical level, the simple linear regression model is a five-parameter model. It is…
The problem of mean-square optimal linear estimation of linear functionals which depend on the unknown values of a multidimensional stationary stochastic sequence from observations of the sequence with a noise and missing observations is…
We propose a test of many zero parameter restrictions in a high dimensional linear iid regression model with $k$ $>>$ $n$ regressors. The test statistic is formed by estimating key parameters one at a time based on many low dimension…
Significant attention has been given to minimizing a penalized least squares criterion for estimating sparse solutions to large linear systems of equations. The penalty is responsible for inducing sparsity and the natural choice is the…
We address the problem of detection and estimation of one or two change-points in the mean of a series of random variables. We use the formalism of set estimation in regression: To each point of a design is attached a binary label that…
This paper considers estimation of sparse covariance matrices and establishes the optimal rate of convergence under a range of matrix operator norm and Bregman divergence losses. A major focus is on the derivation of a rate sharp minimax…
We study sparse group Lasso for high-dimensional double sparse linear regression, where the parameter of interest is simultaneously element-wise and group-wise sparse. This problem is an important instance of the simultaneously structured…
The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…
As neural networks become more popular, the need for accompanying uncertainty estimates increases. There are currently two main approaches to test the quality of these estimates. Most methods output a density. They can be compared by…
Under a standard assumption in complexity theory (NP not in P/poly), we demonstrate a gap between the minimax prediction risk for sparse linear regression that can be achieved by polynomial-time algorithms, and that achieved by optimal…
We consider the problem of estimating a smooth functional of an unknown signal with discontinuity from Gaussian observations. The signal is a known function that depends on an unknown parameter. This problem is closely related to the famous…
In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral/regularized algorithms,…
Sparse recovery is among the most well-studied problems in learning theory and high-dimensional statistics. In this work, we investigate the statistical and computational landscapes of sparse recovery with $\ell_\infty$ error guarantees.…
We study the detection of a change in the covariance matrix of $n$ independent sub-Gaussian random variables of dimension $p$. Our first contribution is to show that $\log\log(8n)$ is the exact minimax testing rate for a change in variance…