Related papers: Inference for concave distribution functions under…
We consider deconvolution from repeated observations with unknown error distribution. So far, this model has mostly been studied under the additional assumption that the errors are symmetric. We construct an estimator for the non-symmetric…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
In the context of linear regression, we construct a data-driven convex loss function with respect to which empirical risk minimisation yields optimal asymptotic variance in the downstream estimation of the regression coefficients. At the…
A generic out-of-sample error estimate is proposed for robust $M$-estimators regularized with a convex penalty in high-dimensional linear regression where $(X,y)$ is observed and $p,n$ are of the same order. If $\psi$ is the derivative of…
For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode…
This paper studies the non-parametric estimation and uniform inference for the conditional quantile regression function (CQRF) with covariates exposed to measurement errors. We consider the case that the distribution of the measurement…
We consider a circular deconvolution problem, in which the density $f$ of a circular random variable $X$ must be estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y$ of $X$. The additive measurement error is…
In this paper, we consider a partial deconvolution kernel estimator for nonparametric regression when some covariates are measured with error while others are observed without error. We focus on a general and realistic setting in which the…
Nonparametric maximum likelihood estimators (MLEs) in inverse problems often have non-normal limit distributions, like Chernoff's distribution. However, if one considers smooth functionals of the model, with corresponding functionals of the…
Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…
In this work we study the estimation of the density of a totally positive random vector. Total positivity of the distribution of a random vector implies a strong form of positive dependence between its coordinates and, in particular, it…
Given noisy data, function estimation is considered when the unknown function is known a priori to consist of a small number of regions where the function is either convex or concave. When the number of regions is unknown, the model…
In Statistics, log-concave density estimation is a central problem within the field of nonparametric inference under shape constraints. Despite great progress in recent years on the statistical theory of the canonical estimator, namely the…
The functional delta-method provides a convenient tool for deriving the asymptotic distribution of a plug-in estimator of a statistical functional from the asymptotic distribution of the respective empirical process. Moreover, it provides a…
A popular approach for estimating an unknown signal from noisy, linear measurements is via solving a so called \emph{regularized M-estimator}, which minimizes a weighted combination of a convex loss function and of a convex (typically,…
In this paper, we further develop the approach, originating in [14 (arXiv:1311.6765),20 (arXiv:1604.02576)], to "computation-friendly" hypothesis testing and statistical estimation via Convex Programming. Specifically, we focus on…
This paper considers inference for a function of a parameter vector in a partially identified model with many moment inequalities. This framework allows the number of moment conditions to grow with the sample size, possibly at exponential…
We study the problem of nonparametric estimation under $\bL_p$-loss, $p\in [1,\infty)$, in the framework of the convolution structure density model on $\bR^d$. This observation scheme is a generalization of two classical statistical models,…
We study the distribution and uncertainty of nonconvex optimization for noisy tensor completion -- the problem of estimating a low-rank tensor given incomplete and corrupted observations of its entries. Focusing on a two-stage estimation…
We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume…